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Question

# X takes 3 hours more than Y to walk 30 km. But, if X doubles his pace, he is ahead of Y by 112 hours. Find their speed of walking.

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Solution

## Let the speed of X and Y be x km/hr and y km/hr respectively. Then,Time taken by X to cover 30km =30xhrs,and, Time taken by Y to cover 30km =30yhrsBy the given conditions, we have30x−30y=3⇒10x−10y=1 .(i)If X doubles his pace, then speed of X is 2x km/hrTimes taken by X to cover 30 km =302xhrsTimes taken by Y to cover 30km =30yhrsAccording to the given conditions, we have30y−302x=112⇒30y−302x=32⇒10y−5x=12⇒−10x+20y=1 .(ii)Putting 1x=u and 1y=v, in equations (i) and (ii) we get10u−10v=1⇒10u−10v−1=0 (iii)−10u+20v=1⇒−10u+20v−1=0 (iv)Adding equations (iii) and (iv), we get10v−2=0⇒v=15Putting v=15 in equation (iii), we get10u−3=0⇒u=310Now, u=310⇒1x=310⇒x=103 and, v=15⇒1y=15⇒y=5Hence, X's speed =103 km/hr and, Y's speed =5 km/hr.

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