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

Answer:

Speed of first skier = 5 km/h

Speed of second skier = 10 km/h

Step-by-step 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 = $Speed\times time=x\times 2=2x\ km$

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

Distance traveled by second skier after 2 hours will be = $Speed\times time=(x+5)\times 2=(2x+10)\ km$   [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.

$\frac{4x}{4}=\frac{20}{4}$

$x=5$

Speed of first skier = 5 km/h

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