# In an 80 km biathlon, a competitor completes the bicycle leg in 2 hours and the running leg in 40 minutes. If the competitor cycles 20 km/h faster than he runs, at what speed does he cycle?

Jun 10, 2018

35km/h

#### Explanation:

We know that the total distance d = 80km.

We also know that we cycle 2h at a v km/h velocity, and 2/3h (40min) at a (v-20)km/h velocity.

Then, we can say calculate the distance that we cycle and the distance that we run:

2hv km/h = km that we cycle
2/3h
(v-20)km/h = km that we run

Then, since we know that the addition of both are the 80km... we can create an equation and solve it:
$2 v + \frac{2}{3} \left(v - 20\right) = 80 \text{ "->" " cancel(2) (v+(v20)/3)=cancel(80)^"40} \downarrow$

$3 \cdot \left(v + \frac{v - 20}{3}\right) = 3 \cdot 40 \text{ "->" } 3 v + v - 20 = 120 \downarrow$

$4 v = 140 \text{ "->" } v = 35 \frac{k m}{h}$

We must bare in mind that it is a very high velocity for a runner.