The distance between points A and B a cyclist can travel 5 hours faster than a pedestrian

The distance between points A and B a cyclist can travel 5 hours faster than a pedestrian. The cyclist’s speed is 12 km / h and the walking speed is 37.5% of the cyclist’s speed. Find the distance from A to B.

Let’s determine the speed of the pedestrian. To do this, we find 35.5% of the cyclist’s speed: 12: 100 · 37.5 = 4.5 (km / h).

Let the time during which the cyclist overcomes the distance between points A and B is x (x) hours, then the pedestrian will cover the same distance in: (x + 5) hours.

Knowing the time and speed of movement of a pedestrian and a cyclist, we express the distance between points and compose the equation:

12 x = 4.5 (x + 5);

12 x = 4.5 x + 22.5;

12 x = 4.5 x + 22.5;

12 x – 4.5 x = 22.5;

7.5 x = 22.5;

x = 22.5: 7.5;

x = 3 (h) – time of movement of the cyclist.

Find out the distance between points between A and B: (12 x) = 12 3 = 36 (km).

Answer: the distance between points A and B is 36 km.