A boy X can run with a speed of 8 ${{ms}^{-1}}$ against the frictional force of 10 N and another Y can move with a speed of 3 ${{ms}^{-1}}$ against the frictional force of 20 N. Find the ratio of powers of X and Y.

Given, distance travelled by the boy X in 1 s = 8 m

Distance travelled by the boy Yin 1 s = 3 m

As we know, work done by the boy X to run against the frictional force ofl0N = 10N X 8m=80J

So, power of 80 J of work done by X =W/t = 80J / 1s = 80 W

Similarly, work done by the boy Y to run against the frictional force of 20 N = 20 N X 3 m= 60J

Power of Y = 60J/1s = 60 W

So, ratio of two values of powers is given by Power of X/ Power of Y = 80 /60 = 4/ 3 = 4 : 3