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Question

A takes 3 hour more than B to walk 30km. But if A doubles his pace, he is ahead of B by 32hours. Find their speed of walking.


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Solution

Step 1. Finding equation using first condition

Let speed of A =xkm/h & speed of B =ykm/h

Therefore ,Time taken by A to cover 30km=30xh [Time=Distancetime]

and time taken by B to cover 30km =30yh

According to question,

30x=30y+3

30x-30y=3--------------------------(i)

Step 2. Finding equation using second condition

When A doubles his speed, then the time taken by A=302x

According to question,

30y=302x+32

-302x+30y=32-

-15x+30y=32-------------------------(ii)

Step 3. Solving equations

Let us assume that 1x=a&1y=b

So equation (i) and equation (ii) becomes
30a-30b=3----------------------(iii)
-15a+30b=32---------------------(iv)

On adding equation(iii) and (iv) we get,

15a=92a=92x15a=310

Substituting a=310 in equation(iii) we get

3031030b=3

930b=3

-30b=-6b=15

Now as we assumed earlier , 1y=b

So we have 1y=15

y=5km/h

And 1x=a

1x=310

x=103km/h

Hence
Speed of A=103km/h
Speed of B=5km/h


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