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. The speed of X is:
103 km/hr
Let the speed of X and Y be x km/hr and y km/hr respectively.
Then, Time taken by X to cover 30 km = 30xhr
and time taken by Y to cover 30 km = 30yhr
From the given conditions, we have
30x−30y=3
⇒10x−10y=1.....(i)
If X doubles his pace then the speed of X is 2x km/hr.
Time taken by X to cover 30 km =302xhr
We have,
30y−302x=112
⇒30y−302x=32
⇒10y−5x=12
⇒−10x+20y=1......(ii)
Let 1x=u and 1y=v.
In equation (i) and (ii), we get:
10u−10v=1⇒10u−10v−1=0......(iii)
and −10u+20v=1⇒−10u+20v−1=0.....(iv)
Adding equations (iii) and (iv), we get
10v−2=0⇒v=15
Putting v=15 in equation (iii), we get
⇒10u−1013−1=0
⇒10u−3=0⇒u=310
Now,u=310
⇒1x=310
⇒x=103
∴ X's speed is 103km/hr.