A takes 3 hours more than B to walk 30 km. But if A . . .

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

Doubt by Jaskirat

Solution : 

Let the speed of walking of A = x km/h

and the speed of walking of B = y km/h

Distance covered by both A and B = 30 km

We know, 
Speed = Distance/Time

Time = Distance/Speed

Time taken by A to cover the distance of 30 km
t₁=30/x hr
Time taken by B to cover the distance of 30 km

t₂=30/y hr

ATQ

t₁=3+t₂

t₁-t₂ = 3

30/x - 30/y = 3 

30[1/x-1/y]=3
1/x-1/y=3/30 
1/x-1/y=1/10 — (1)

When A doubles his pace then his speed will become 2x km/h

Speed of B remains same as y km/h

Then 

Time taken by A to cover the distance of 30 km
t₁=30/2x hr
Time taken by B to cover the distance of 30 km

t₂=30/y hr

ATQ

t₂=t₁+3/2
t₂-t₁=3/2

30/y-30/2x=3/2
30[1/y-1/2x]=3/2

1/y-1/2x=1/20

-1/2x+1/y=1/20 — (2) 

On solving equation (1) and (2) by elimination method we get x=10/3 km/h and y=5 km/h.

The speed of walking of A is 10/3 = 3.33 km/h while the speed of walking of B is 5 km/h.