Question

A takes 3 hours more than B to walk 30km. But if A doubles his pace , he is ahead of B by 3/2 hours . Find their speed of walking.

Answer 1

GIVEN : Distance = 30 km 
Let speed of A be = x km/h &  speed of B = y km/h.
Time taken by A to cover 30  km = 30/x[ Time = Distance /speed]
Time taken by B to cover 30 km = 30/y30/x = 30/y + 330/x - 30/y = 3…………(1)[Given : A takes 3 hours more than B to walk ]
When A doubles his speed then, time taken by A = 30/2x [Given: time taken by B =  Time taken by A + 3/2 h]30/y = 30/2x + 3/230/y - 30/2x  = 3/2 30/y - 15/x  = 3/2 ……..(2)
Let  1/x= p  and 1/y = q
so eqs 1 & 2 become ,then On adding eq 3 & 430p -  30q = 3……….(3)-15p +  30q = 3/2………(4) ---------------------------15 p = 3 + 3/2 
15 p =( 6 + 3)/2 = 9/2 15p = 9/2p = 9 /(2×15) = 3/10p = 3/10
On Putting the value of p = 3/10 in eq 330p -  30q = 330 (3/10) - 30q = 39 - 30q = 39 - 3 = 30q6 = 30q
q = 6/30= 1/51/y = q               [ Let 1/y = q]1/y = ⅕ y = 5 km/h
1/x = p             [Let 1/x= p ]1/x = 3/10x = 10/3 km/h
so x = 10/3 km/h. &  y = 5 km/h
Hence, the speed of A is 10/3 km/h & B is 5 km/h.