Two runners simultaneously in the same direction. Did the two runners start in the same direction at the same time from the same place? What do we have to do

Question: Two runners started simultaneously in the same direction from the same place on the track for multiple laps. One hour later, when one of them had 3 km left before the end of the first lap, he was informed that the second runner had completed the first lap 6 minutes ago. Find the speed of the first runner if it is known that it is 5 km / h less than the speed of the second.

Two runners started at the same time in the same direction from the same place on the track for several laps. One hour later, when one of them had 3 km left before the end of the first lap, he was informed that the second runner had completed the first lap 6 minutes ago. Find the speed of the first runner if it is known that it is 5 km / h less than the speed of the second.

Answers:

Let the speed of the first runner be x km / h, the second x + 5 km / h. The first runner ran in 1 hour: S (distance) \u003d v (speed) * t (time) \u003d x * 1 \u003d x km The second ran the circle 6 minutes earlier, i.e. in 54 minutes \u003d 54/60 \u003d 9/10 hours. During this time, he ran: S \u003d (x + 5) * 9/10 km, which is 3 km more than the first runner. (x + 5) * 9/10-x \u003d 3 9 / 10x + 9/2 - x \u003d 3 0.9x + 4.5-x \u003d 3 -0.1x \u003d 3-4.5 -0.1x \u003d 3-4.5 -0.1x \u003d -1.5 x \u003d 15 km / h - the speed of the first runner. Answer: the speed of the first runner is 15 km / h.

What do we have to do?

Each of you can control your runner, who can move on any surface by controlling gravity. This is an android man, with a bright haircut and super sneakers, who reacts to your every click. In the game Runner 2 for two, you need to change the direction of gravity in time so as not to fall into the abyss.

Sprinters run themselves. Your path is full of obstacles to overcome. Run as far as possible and become a champion. The game requires great reaction, so all of you will need to show your best attention and try to show your best side. On your marks! Attention! Forward!

Question: Two runners started at the same time in the same direction from the same spot on a multi-lap track. One hour later, when one of them was 3 km away. before the end of the first lap, he was informed that the second runner had completed the first lap 6 minutes ago. Find the speed of the first runner if it is known that it is 5 km / h less than the speed of the second.

Two runners started at the same time in the same direction from the same place on the track in a multi-lap race. One hour later, when one of them was 3 km away. before the end of the first lap, he was informed that the second runner had completed the first lap 6 minutes ago. Find the speed of the first runner if it is known that it is 5 km / h less than the speed of the second.

Answers:

Let x km / h be the speed of the first runner. Then the speed of the second (x + 5) km / h. Because it is known that the second runner ran the first lap 6 minutes before the end of the first hour of the race, then he ran the first lap in 0.9 hours (since 6 minutes \u003d 0.1 hours). Those. the length of the circle is 0.9 (x + 5). On the other hand, the length of the circle is 1 * x + 3, because in one hour the first one did not reach the end of the circle 3 km. So, we get the equation x + 3 \u003d 0.9 (x + 5). We solve it: x + 3 \u003d 0.9x + 4.5 x-0.9x \u003d 4.5-3 0.1x \u003d 1.5 x \u003d 15. Answer: the speed of the first is 15 km / h.

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Two runners simultaneously started in the same direction from the same
places of the circular track. Later one hourwhen one of them remained 0.6 miles
before the end of the first lap, he was informed that the second runner had passed the first
a circle 5 minutes back. Find the speed of the first runner if known
what is she at 2 km / h less than the speed of the second.

A circular track or a straight line - in this task it does not matter.

Let's stop time an hour after the start. Interesting that paths that runners
ran in an hour, are numerically equal to their speeds... Let's take advantage of this fact.

It follows from the condition that the second runner ran two kilometers more in one hour first.
But the first one remained to the finish line 0.6 miles... This means that the second ran away from the finish line by the same 1 km.

And the second runner covered this very kilometer in five minutes, as the first was told.
Finding the speed of the second is now easy. If in 5 minutes he runs 1 kilometer, then
he will run in an hour 12 times more, i.e. 12 kilometers. Its speed 12 km / h.
Well, the speed of the first runner by 2 km / h less, i.e. equals 10 km / h.

Answer: 10 km / h

Let's solve the problem using an equation, denoting the speed of the runners accordingly.

The path that ran the second in 55 minutes (from start to finish) is 1 km more,
than the path that ran in the first hour (he did not run a kilometer to the finish line).

From here we find that x \u003d 10.

1.MOVING IN A CIRCLE

17.3-6. Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 1 km before the end of the first lap, he was informed that the second runner had completed the first lap 20 minutes ago. Find the speed of the first runner if it is known that it is 7 km / h less than the speed of the second.

V t S Equation: 2/3 (X + 7) - X \u003d 1 hence X \u003d 11.

X 1 hour X

X + 7 2/3 h 2/3 (X + 7)

85.3-12. Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 5 km before the end of the first lap, he was informed that the second runner had completed the first lap 6 minutes ago. Find the speed of the first runner if it is known that it is 7 km / h less than the speed of the second.

V t S Equation: 0.9 (X + 7) - X \u003d 5 hence X \u003d 13.

X 1 hour X

X + 7 0.9 h 0.9 (X + 7)

294. 3.63 (1). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 1 km before the end of the first lap, he was informed that the second runner had completed the first lap 20 minutes ago. Find the speed of the first runner if it is known that it is 8 km / h less than the speed of the second.

V t S Equation: 2/3 (X + 8) -X \u003d 1, X \u003d 13.

X 1 hour X

X + 8 2 / 3h 2/3 (X + 8)

3.63 (2). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 1 km before the end of the first lap, he was informed that the second runner had completed the first lap 15 minutes ago. Find the speed of the first runner if it is known that it is 5 km / h less than the speed of the second.

V t S

X 1 hour X

X + 5 3/4 h 3/4 (X + 5), Equation: 3/4 (X + 5) -X \u003d 1, X \u003d 11

3.63 (3). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 7 km before the end of the first lap, he was informed that the second runner had completed the first lap 3 minutes ago. Find the speed of the first runner if it is known that it is 8 km / h less than the speed of the second.

V t S

X 1 hour X

X + 8 19/20 h (X + 8) 19/20, Equation: 19/20 (X + 8) -X \u003d 7, X \u003d 12

297. 3.63 (4). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 1 km before the end of the first lap, he was informed that the second runner had completed the first lap 3 minutes ago. Find the speed of the first runner if it is known that it is 2 km / h less than the speed of the second.

V t S

X 1 hour X

X + 2 19/20 h (X + 2) 19/20, Equation: 19/20 (X + 2) -X \u003d 1, X \u003d 18

298. 3.63 (5). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 4 km before the end of the first lap, he was informed that the second runner had completed the first lap 20 minutes ago. Find the speed of the first runner if it is known that it is 11 km / h less than the speed of the second.

V t S

X 1 hour X

X + 11 2/3 h 2/3 (X + 8) Equation: 2/3 (X + 8) - X \u003d 4, X \u003d 10.

3.63 (6). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 2 km before the end of the first lap, he was informed that the second runner had completed the first lap 4 minutes ago. Find the speed of the first runner if it is known that it is 3 km / h less than the speed of the second.

V t S

X 1 hour X

X + 3 14/15 h 14/15 (X + 3) Equation: 14/15 (X + 3) -X \u003d 2, X \u003d 12

3.63 (7). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 1 km before the end of the first lap, he was informed that the second runner had completed the first lap 15 minutes ago. Find the speed of the first runner if it is known that it is 6 km / h less than the speed of the second.

V t S

X 1 hour X

X + 6 3 / 14h 3/14 (X + 6) Equation: 3/14 (X + 6) –X \u003d 4, X \u003d 14

3.63 (8). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 6 km before the end of the first lap, he was informed that the second runner had completed the first lap 9 minutes ago. Find the speed of the first runner if it is known that it is 9 km / h less than the speed of the second.

V t S

X 1 hour X

X + 9 17/20 h 17/20 (X + 9) Equation: 17/20 (X + 9) -X \u003d 6, X \u003d 11.

3.63 (9). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 2 km before the end of the first lap, he was informed that the second runner had completed the first lap 20 minutes ago. Find the speed of the first runner if it is known that it is 9 km / h less than the speed of the second.

V t S

X 1 hour X

X + 9 2 / 3h 17/20 (X + 9) Equation: 2/3 (X + 9) -X \u003d 2, X \u003d 12.

3.63 (10). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 5 km before the end of the first lap, he was informed that the second runner had completed the first lap 10 minutes ago. Find the speed of the first runner if it is known that it is 8 km / h less than the speed of the second.

V t S

X 1 hour X

X + 8 5 / h 5/6 (X + 8) Equation: 5/6 (X + 8) - X \u003d 5, X \u003d 10.

3.63 (11). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 8 km before the end of the first lap, he was informed that the second runner had completed the first lap 3 minutes ago. Find the speed of the first runner if it is known that it is 9 km / h less than the speed of the second. V t S

X 1 hour X

X + 9 19 / 20h 19/20 (X + 9) Equation: 19/20 (X + 9) - X \u003d 8, X \u003d 11.

3.63 (12). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 2 km before the end of the first lap, he was informed that the second runner had completed the first lap 24 minutes ago. Find the speed of the first runner if it is known that it is 10 km / h less than the speed of the second.ANSWER: 10

3.63 (13). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 1 km before the end of the first lap, he was informed that the second runner had completed the first lap 30 minutes ago. Find the speed of the first runner if it is known that it is 12 km / h less than the speed of the second.ANSWER: 10

3.63 (14). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 5 km before the end of the first lap, he was informed that the second runner had completed the first lap 6 minutes ago. Find the speed of the first runner if it is known that it is 7 km / h less than the speed of the second. ...ANSWER: 13

3.63 (15). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 3 km before the end of the first lap, he was informed that the second runner had completed the first lap 9 minutes ago. Find the speed of the first runner if it is known that it is 6 km / h less than the speed of the second. ...ANSWER: 24

3.63 (16). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 4 km before the end of the first lap, he was informed that the second runner had completed the first lap 18 minutes ago. Find the speed of the first runner if it is known that it is 10 km / h less than the speed of the second. ...ANSWER: 10

310. 3.63 (17). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 2 km before the end of the first lap, he was informed that the second runner had completed the first lap 9 minutes ago. Find the speed of the first runner if it is known that it is 5 km / h less than the speed of the second. ...ANSWER: 15

3.63 (18). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 4 km before the end of the first lap, he was informed that the second runner had completed the first lap 6 minutes ago. Find the speed of the first runner if it is known that it is 6 km / h less than the speed of the second. ...ANSWER: 14

3.63 (19). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 1 km before the end of the first lap, he was informed that the second runner had completed the first lap 20 minutes ago. Find the speed of the first runner if it is known that it is 7 km / h less than the speed of the second. ...ANSWER: 11

V t S

X 1 hour X

X + 7 2/3h 2/3 (X + 7) Equation: 2/3 (X + 7) -X \u003d 1. X \u003d 11

313. 3.63 (20). Two runners started at the same time in the same direction from the same place on the circuit in a multi-lap race. One hour later, when one of them had 3 km before the end of the first lap, he was informed that the second runner had completed the first lap 6 minutes ago. Find the speed of the first runner if it is known that it is 5 km / h less than the speed of the second.ANSWER: 15 563.B 14 No. 99596. Two motorcyclists start simultaneously in the same direction from two diametrically opposite points of the circular track, the length of which is 14 km. In how many minutes will motorcyclists level up for the first time if one of them is 21 km / h faster than the other?Decision ... Let V km / h be the speed of the first motorcyclist, then the speed of the second motorcyclist is (V + 21) km / h. Let the motorcyclists level up for the first time in hours. In order for the riders to catch up, the faster one must cover the distance initially separating them, equal to half the length of the track. Therefore (V + 21) t-Vt \u003d 7, 21t \u003d 7, t \u003d ... Thus, motorcyclists will level up through hours or 20 minutes later. Answer: 20.

Let's give another solution... A fast motorcyclist moves a relatively slow one at a speed of 21 km per hour, and must overcome the 7 km separating them. Therefore, it will take him one third of an hour. 564.B 14 No. 99598. From one point of the circular track, the length of which is 14 km, two cars started simultaneously in the same direction. The speed of the first car is 80 km / h, and 40 minutes after the start, it was one lap ahead of the second car. Find the speed of the second car. Give your answer in km / h.Decision. Let the speed of the second car be V km / h. In 2/3 hours, the first car covered 14 km more than the second, hence we have 80V + 14, 2V \u003d 80 V \u003d 59. Answer: 59. 565.B 14 No. 99599. A cyclist left point A of the circular track, and after 30 minutes a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and 30 minutes later he caught up with him a second time. Find the speed of the biker if the track is 30 km long. Give your answer in km / h.Decision. By the time of the first overtaking, the motorcyclist traveled in 10 minutes as much as the cyclist in 40 minutes, therefore, his speed is 4 times higher. Therefore, if the speed of the cyclist is taken as x km / h, then the speed of the motorcyclist will be 4x, and the speed of their approach is 3x km / h. On the other hand, the second time a motorcyclist caught up with a cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, the speed of their convergence is 60 km / h. So, 3x \u003d 60 km / h, whence the speed of the cyclist is 20 km / h, and the speed of the motorcyclist is 80 km / h. 566.B 14 No. 99600. The clock with hands shows 8 hours 00 minutes. In how many minutes will the minute hand align with the hour hand for the fourth time?Decision ... The speed of the minute hand is 12 divisions / hour (one division here means the distance between adjacent digits on the clock face), and the hour hand is 1 division / hour. Before the fourth meeting of the minute and hour hands, the minute must first “overtake” the hour hand 3 times, that is, go through 3 circles of 12 divisions. Let after that, until the fourth meeting, the hour hand will go through L divisions. Then the general path of the minute hand consists of the 36 divisions found, 8 more divisions initially separating them (since the clock shows 8 o'clock) and the last L divisions. Let's equate the movement time for the hour and minute hands:= , 12 L \u003d L + 44, L \u003d 4 The hour hand will move through 4 divisions, which corresponds to 4 hours, that is, 240 minutes. Answer: 240.Let's give another solution... It is clear that the first time the hands will meet between 8 and 9 o'clock, the second time - between 9 and 10 o'clock, the third - between 10 and 11, the fourth - between 11 and 12 o'clock, that is, at exactly 13 o'clock. Thus, they will meet in exactly 4 hours, which is 240 minutes.At the request of readers, we publish a general solution.The rotation speed of the hour hand is 0.5 degrees per minute, and the minute hand is 6 degrees per minute. Therefore, when the clock shows time h hours m minutes, the hour hand is rotated by 30h + 0.5m degrees, and the minute hand - by 6m degrees relative to the 12-hour division. Let the arrows meet for the first time through minutes. Then if the minute hand has not yet advanced the hour hand during the current hour, then 6m + 6 \u003d 30h + 0.5m + 0.5, i.e. \u003d (60h - 11m) / 11 (*). Otherwise, we get the equation 6m + 6 \u003d 30h + 0.5m + 0.5 + 360, whence \u003d (60h - 11m + 720) / 11 (**). Let the arrows meet the second time t2 minutes after the first, then 0.5t2 \u003d 6t2 - 360, whence \u003d 720/11 (***). The same is true for every next turn. Therefore, for a meeting with number n from (*) and (**), taking into account (***), we have, respectively: \u003d (60h - 11m + 720 (n - 1)) / 11 or \u003d (60h - 11m + 720n) / 11. 567.B 14 No. 323856. Two drivers are racing. They will have to drive 60 laps along a 3 km long circular track. Both riders started at the same time, and the first came to the finish line 10 minutes earlier than the second. What was the average speed of the second rider if it is known that the first rider for the first time overtook the second by a lap in 15 minutes?Decision. The first overtook the second by 3 km in a quarter of an hour, which means that the speed of removal (convergence) of the riders is 3 km / h. Let's designate the speed of the second rider X km / h, then the speed of the first (X + 12) km / h. Having compiled and solved the equation where 180 km is the length of the entire track, 10 minutes \u003d hours, we get that the speed of the second rider is 108 km / h.Answer: 108. Note. The task does not specify in what units to indicate the found speed. We have already contacted the Open Bank developers and informed them about it.