Question

‘A’ takes 3 hours more than ‘B’ to walk 30 km . But if A doubles his pace , he is ahead of B by 1 1/2 hours . Find their speeds of walking

Answer 1

Answer:

S / Ra = Ta    where S = 30 km, Ra = speed of A and Ta = time for A to walk S

S / Rb = Tb

Ta - Tb = S * (1 / Ra - 1 / Rb) = S * (Rb - Ra) / (Ra Rb) = 3    (I)

Likewise  S * (2 Ra - Rb) / (2 Ra Rb) = 1.5 if A doubles his pace

So (Rb - Ra) / (Ra Rb) =  (2 Ra - Rb) / ( Ra Rb)

and 3 Ra = 2 Rb   or Ra = 2/3 Rb

3 / 30 = (Rb - 2 Rb / 3) / (2 /3 Rb * Rb)  from (I)

(1 / 3) / (2 Rb /3) = 1/10

So Rb = 5 km/hr   and Ra = 10 / 3 km/hr

Tb = 30 / 5 = 6 hr    Ta = 30 / (10 /3) = 9 hr

If A doubles his pace then Ra = 20 / 3 km/hr

and Ta = 30 / (20 /3) = 4 1/2 hrs