From two points A and B, the distance between which is 10 km, a cyclist and a motorcyclist left simultaneously

| March 23, 2021 | education

From two points A and B, the distance between which is 10 km, a cyclist and a motorcyclist left simultaneously and in the same direction in such a way that the motorcyclist overtakes the cyclist. After 2/3 hours, the distance between them was 10 km. Find the speed of the cyclist if it is known that it is 3 times less than the speed of the motorcyclist.

Let x km / h be the speed of the cyclist, then 3 km / h is the speed of the motorcyclist.

It is known that the motorcyclist overtook the cyclist in 2/3 hours. During this time the motorcycle traveled 3x * 2/3 = 2x km, and the bicycle – 2x / 3 km.

Since the motorcyclist first reduced the distance to the cyclist, equal to 10 km, and then overtook him by 10 km, then in total he drove 10 + 2x / 3 + 10 = 2x / 3 + 20 km.

Let’s compose and solve the equation.

2x = 2x / 3 + 20,

2x – 2x / 3 = 20,

4x / 3 = 20,

x = 20 * 3/4,

x = 15.

Answer: the speed of the cyclist is 15 km / h.



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