The cyclist traveled the distance between points A and B in 3 hours. On the way back, he increased the speed by 2 km / h.

The cyclist traveled the distance between points A and B in 3 hours. On the way back, he increased the speed by 2 km / h. Therefore, the cyclist spent 30 minutes less on this path. At what speed did the cyclist go from point A to point B?

1. Suppose that the speed of the cyclist on the way from point A to point B was x km per hour.

2. Being on the way for 3 hours, he traveled the path (x * 3) = 3 km.

3. On the way back, the cyclist was driving at a speed of (x + 2) km per hour.

4. Since the cyclist spent 30 minutes less on the way back, therefore he was on the way for 3 hours – 30 minutes = 2 hours 30 minutes or 2.5 hours.

5. The path he traveled on the way back is 2.5 * (x + 2) km.

6. Let’s make an equation and find out the speed of the cyclist on the path and point A to point B, if both paths are equal.

3x = 2.5 * (x + 2);

3x = 2.5x + 5;

3x – 2.5x = 5;

0.5x = 5;

x = 5 / 0.5;

x = 10 km per hour.

Answer: The speed of a cyclist on the way from point A to point B is 10 km per hour.