A cyclist and a motorcyclist left point A to point B at the same time. The speed of the cyclist is 15 km / h

A cyclist and a motorcyclist left point A to point B at the same time. The speed of the cyclist is 15 km / h, and the speed of the motorcyclist is 24 m / h. But 4 hours after starting the movement, the motorcyclist’s engine stalled. Having repaired it, I moved on and caught up with the cyclist in 1 hour. How long has a motorcyclist been fixing his engine?

1. Cyclist speed: Vв = 15 km / h;
2. Motorcyclist speed: Vm = 24 km / h;
3. The engine stalled after a time: T1 = 4 hours;
4. After the repair, the motorcyclist caught up with the cyclist in time: T2 = 1 hour;
5. The distance traveled by the motorcyclist to the engine breakdown: Sв1 km;
Sw1 = Vw * T1 = 15 * 4 = 60 km;
6. Distance covered by the cyclist during the same time: Sм1 km;
Sm1 = Vm * T1 = 24 * 4 = 96 km;
7. Engine repair time: Tr hour;
8. During the repair, the cyclist traveled more: Svr km;
Svr = (Vw * Tr) km;
9. The total distance traveled by the cyclist: Swo km;
Svo = Sv1 + Svr = (60 + Vv * Tr) km;
10. To catch up with the cyclist, the motorcyclist must drive the distance: Sd km;
Sd = Swo – Sm1 = (60 + Vw * Tr) – 96 = Vw * Tr – 36 km;
11. Difference speed of a motorcyclist and a cyclist:
V = Vm – Vv = 24 -15 = 9 km / h;
12. The time it takes for the motorcyclist to catch up with the cyclist: Td hour;
Td = Sd / V = ​​(Vw * Tr – 36) / 9 = 1 hour;
Vw * Tr – 36 = 9;
Tr = 45 / Vv = 45/15 = 3 hours.
Answer: engine repair lasted 3 hours.