One skier covered the distance of 20 km 20 minutes faster than the other skier. find the speed of both skiers if one of them is travelling 2 km/hour faster than the other one.

Distance covered = 20 km

Let x km/h be the speed pf first sky. Then, speed of second sky will be (x+2) km/h

Time = distance/speed

Therefore,

20/x - 20 / (x+2) = 20 minutes = 1/3 hrs

Solving;

20 (x+2) - 20 (x) = x (x+2) * 1/3

60 (x+2) - 60 (x) = x^2+2x

60x+120-60x = x^2+2x

120 = x^2+2x

x^2+2x-120 = 0

Then,

x = {-b + / - sqrt (b^2-4ac) }/2a = {-2 + / - sqrt (2^2-4*a*-12) } / (2*1) = 10 or - 12

Ignoring the negative value, x = 10 km/h

Therefore, the first sky is travelling at 10 km/h while the second is travelling at (10+2) 12 km/h