A running man has half the kinetic energy than a boy of half his mass has. The man speeds up by I m/sec and then has the same kinetic energy as the boy. What were the original speeds of man and boy respectively?

Let, M = mass of man, m = mass of boyV = speed of man, v = speed of boyGiven: 12MV2 = 12(12mv2), As m = M2So 12MV2 = 12(12×M2v2), Hence, v2 = 4V2 or v =2 VWhen the man speeds up by I m./s, then we get12M(V+1)2 = 12mv2 = 12M2(4V2)or (V+1)2 = 2V2 or V2-2V-1 = 0Solving we get: V:2.4 m/s and v : 4.8 m/s