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](https://tex.z-dn.net/?f=x)
<em>Distance covered in km 2 hours will be =
</em>
Speed of second skier in km/h can be given as = ![x+5](https://tex.z-dn.net/?f=x%2B5)
<em>Distance traveled by second skier after 2 hours will be =
[Using distribution]</em>
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](https://tex.z-dn.net/?f=2x%2B2x%2B10%3D30)
Solving for ![x](https://tex.z-dn.net/?f=x)
![4x+10=30](https://tex.z-dn.net/?f=4x%2B10%3D30)
Subtracting both sides by 10.
![4x+10-10=30-10](https://tex.z-dn.net/?f=4x%2B10-10%3D30-10)
![4x=20](https://tex.z-dn.net/?f=4x%3D20)
Dividing both sides by 4.
![\frac{4x}{4}=\frac{20}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B4x%7D%7B4%7D%3D%5Cfrac%7B20%7D%7B4%7D)
![x=5](https://tex.z-dn.net/?f=x%3D5)
Speed of first skier = 5 km/h
Speed of second skier =
= 10 km/h