The motorcyclist traveled 75% of the distance from point N to point M at a speed of v1. Having increased the speed by 10 m / s

The motorcyclist traveled 75% of the distance from point N to point M at a speed of v1. Having increased the speed by 10 m / s, he reached point M in the same time and returned back to point N. Find the initial speed of the motorcyclist.

Given:

v1 is the speed at which the motorcyclist covered 75% of the distance from point N to M;

v2 = v1 + 10 – the speed with which the motorcyclist reached point M and returned back to point N;

t1 = t2 – the time of movement of the motorcyclist is the same in both cases.

It is required to determine v1 (meter per second) – the initial speed of the motorcyclist.

Let S be the distance between points N and M.

Then we get:

t1 = 0.75 * S / v1;

t2 = (0.25 * S + S) / v2 = 1.25 * S / (v1 + 10).

Since, according to the condition of the problem, the time is the same in both cases, then:

t1 = t2;

0.75 * S / v1 = 1.25 * S / (v1 + 10);

0.75 * S * (v1 + 10) = 1.25 * S * v1;

0.75 * (v1 + 10) = 1.25 * v1;

0.75 * v1 + 7.5 = 1.25 * v1;

1.25 * v1 – 0.75 * v1 = 7.5;

0.5 * v1 = 7.5;

v1 = 7.5 / 0.5 = 15 meters per second.

Answer: The initial speed of the motorcyclist is 15 m / s.