Question

A cyclist cycles non-stop from A to B, a distance of 14 km at a certain average speed. If his average speed reduced by 1 km per hour, he takes `1/3` h more to cover the same distance. Find his original average speed.

Answer 1

Let the original average speed of the cyclist be x km/h.

Distance = 14 km

`14/x` hours

Reduced speed = x − 1 km/h

New time:

`14/(x-1)` hours 

Time increases by `1/3` hour:

`14/(x-1) = 14/x + 1/3`

Multiply both sides by 3x(x − 1):

42x = 42(x − 1) + x(x − 1)

42x = 42x − 42 + x² − x

0 = x² − x − 42

(x − 7) (x + 6) = 0

x = 7 or x = −6

The original average speed of the cyclist is: 7 km/h​