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Question

A man travels 108 km and finds that he could have made the journey in412 hrs less, had he traveled 2 km per hr faster. At what rate did he travel?

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Solution

Let the man travels with speed=x km/h

So time taken to cover the distance of108km=108kmx
If speed increases by 2km/h
Now, speed =x+2

Then time requires to cover, 108km=108kmx+2

these two time has difference of , 412=92h

108x108x+2=92

108x(x+2)108xx(x+2)=92

108x2+216108x(x2+2x)=92

216x2+2x=92

9(x2+2x)=216×2

9x2+18x=432

9x2+18x432=0

x2+2x48=0

x2+8x6x48=0

(x+8)(x6)=0

Since, speed can not be negative, so x=6kmh1



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