Question

Two skiers are 30 kilometers apart and head towards each other. They meet in 2 hours. If the second skier is 5 kilometers per hour faster then the other, find the speed of each skier?

Answer 1

Speed of first skier = 5 km/h

Speed of second skier = 10 km/h

Explanation:

Given:

Distance between skiers = 30 km

Time after which they meet = 2 hours

Second skier is 5 km/h faster than the first skier.

To find speed of each skier.

Solution:

Let the speed of first skier be in km/h =
`x`

Distance covered in km 2 hours will be =
`Speed* time=x* 2=2x\ km`

Speed of second skier in km/h can be given as =
`x+5`

Distance traveled by second skier after 2 hours will be =
`Speed* time=(x+5)* 2=(2x+10)\ km` [Using distribution]

Since, the skiers were 30 km apart initially, so the total distance covered by both of them when they meet after 2 hours will be = 30 km

Thus, we have:

`2x+2x+10=30`

Solving for
`x`

`4x+10=30`

Subtracting both sides by 10.

`4x+10-10=30-10`

`4x=20`

Dividing both sides by 4.

`(4x)/(4)=(20)/(4)`

`x=5`

Speed of first skier = 5 km/h

Speed of second skier =
`5+5` = 10 km/h