Two runners simultaneously started in the same direction from the same place of the circular track

Two runners simultaneously started in the same direction from the same place of the circular track in a run for several laps 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 run 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.

1. The length of the circuit is equal to: L km;

2. Speed ​​of the first runner: V1 km / h;

3. Speed ​​of the second runner: V2 km / h;

4. By the condition of the problem:

V2 = (V1 + 5) km / h;

5. Time of the race from the start: T1 = 1 hour;

6. The first runner has to reach the end of the circle: L2 = 2 km;

7. The second runner finished the circle: T2 = 9 minutes ago;

8. The first runner ran the distance: L1 km;

L1 = L – L2 = L – 2 = V1 * T1;

9. Circle length: L = V1 * T + 2 = (V1 + 2) km;

10. Time, during which the second runner ran a circle: T3 hour;

T3 = T1 – T2 = 1 – 9/60 = 17/20 hours;

But T3 = L / V2 = L / (V1 + 5);

11. Thus: L / (V1 + 5) = 17/20;

L = (17 * (V1 + 5)) / 20;

12. From (9) and (11) we obtain the equation:

V1 + 2 = (17 * (V1 + 5)) / 20;

20 * V1 + 40 = 17 * V1 + 85;

3 * V1 = 45;

V1 = 45/3 = 15 km / h;

V2 = V1 + 5 = 15 + 5 = 20 km / h.

Answer: the speed of the first runner is 15 km / h.