From the village to the city, the distance between which a motorcyclist left 60 km, and 20 minutes

| January 16, 2021 | education

From the village to the city, the distance between which a motorcyclist left 60 km, and 20 minutes later a car drove out after him that arrived in the city 10 minutes earlier than the motorcyclist. Find the speed of the car if it is known that it is 20 km / h more than the speed of the motorcyclist.

1. The distance between the village and the city is: S = 60 km;
2. Vehicle speed is equal to: Va km / h;
3. Motorcyclist speed: Vm km / h;
4. The ratio of speeds: Vm = (Va – 20) km / h;
5. The car left the motorcyclist by: To = 20 minutes = 1/3 hour;
6. He arrived in the city before the motorcyclist by: Tp = 10 minutes = 1/6 hour;
7. Equation of motion in time:
Ta = Tm – To – Tp;
Tm – Ta = To + Tp;
S / Vm – S / Va = (1/3 + 1/6);
60 / (Va – 20) – 60 / Va = 0.5;
Va – Va + 1200 = 0.5 * Va * (Va – 20);
Va² – 20 * Va – 2400 = 0;
Va1,2 = 10 + – sqrt (10² + 2400) = 10 + – 50;
A negative root is meaningless;
Va = 10 + 50 = 60 km / h.
Answer: the vehicle speed is 60 km / h.



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