# A cyclist goes on a 40 km round trip. The cyclists speed going north is 4 kmph more than coming back south. What is the cyclist's speed heading north and south?

Apr 13, 2017

The bicyclist heading north is moving at $18$ km/h and the bicyclist heading south is moving at $14$ km/h.

#### Explanation:

An hour and a quarter has passed and they are $40$ kms apart. By the formula $s = \frac{d}{t} \to d = s \left(t\right)$, letting $x$ be the speed of the south-bound cyclist, we have:

$\frac{5}{4} \left(x + 4\right) + \frac{5}{4} \left(x\right) = 40$

$\frac{5}{4} x + 5 + \frac{5}{4} x = 40$

$\frac{5}{2} x = 35$

$x = \frac{35}{\frac{5}{2}}$

$x = 14$

This means that the cyclist heading south travels at $14$ km/h, and so the cyclist heading north was traveling at $18$ km/h.

Hopefully this helps!