From points A and B, the distance between which is 150 km, a motorcyclist and a cyclist drove

From points A and B, the distance between which is 150 km, a motorcyclist and a cyclist drove towards each other at the same time. Two hours later they met and, without stopping, continued to move. The motorcyclist arrived at point B three hours earlier than the cyclist at point A. Find the speed of the cyclist.

1. We take the speed of the cyclist as x (km / h), the speed of the motorcyclist as y (km / h).

2. Let’s compose a system of equations:

(1) 2x + 2y = 150; x + y = 75; x = 75 – y

(2) 150 / x – 150 / y = 3;

3. Substitute the value x = 75 – y into the second equation:

150 / (75 – y) – 150 / y = 3;

300u – 150 x 75 / (75u – y²) = 3;

300y – 150 x 75 = 225y – 3y².

3y² + 75y – 3750 = 0;

y² + 25y – 3750 = 0;

The first value of y = (- 25 + √625 + 4 x 3750) / 2 = (- 25 + 125) / 2 = 50.

The second value is y = (- 25 – 125) / 2 = – 75. Not accepted

The speed of the motorcyclist is 50 km / h.

Cyclist speed 75 – 50 = 25 km / h.

Answer: the speed of the cyclist is 25 km / h.