A cyclist rode 40 miles before having a flat tire and than walking 5 miles to a service station. The cycling rate was four times the walking rate. The time spent cycling and walking was 5 hours. Find the rate at which the cyclist was riding.

Step-by-step explanation:

Let x represent the walking rate of the cyclist.

If the cycling rate was four times the walking rate, it means that the cycling rate is 4x mph.

Time = distance/speed

Time spent during cycling is

Time = 40/4x = 10/x

Time spent during walking is

5/x

Since the total time spent cycling and walking is 5 hours, it means that

10/x + 5/x = 5

Cross multiplying by x, it becomes

10 + 5 = 5x

5x = 15

x = 15/5

x = 3

The cycling speed is 4x = 4 × 3 = 12 mph