Question

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?

Answer 1

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:
`2v+2/3(v-20)=80 " "->" " cancel(2) (v+(v20)/3)=cancel(80)^"40" darr`

`3*(v+(v-20)/3)=3*40 " "->" " 3v+v-20 = 120 darr`

`4v = 140 " "->" " v=35(km)/h`

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