Q29 of 29 Page 3

X takes 3 hours more than Y to walk 30 km. But if X doubles his pace, he is ahead of Y by 11/2 hours. Find their speed of walking.

Let the speed of X be x km/h and speed of Y is y km/h.


Time taken by X to cover distance of 30 km is hrs.


Time taken by Y to cover distance of 30 km is hrs.


As X takes 3 hours more than Y to walk 30 km,


So,



…… (1)


Now if X doubles his place then time taken is hrs


Time taken by Y to cover distance of 30 km is hrs.


As if X doubles his pace, he is ahead of Y by 11/2 hours,


Also speed of X increases time taken by him will decrease.


So,





……. (2)


Now put


So (1) and (2) become,


10 u – 10v = 1


⇒ 10u – 10v – 1 = 0 ….. (3)


–10u + 20v = 1


⇒ –10u + 20v – 1 = 0 ….. (4)


Adding (3) and (4) we get,


10 u – 10 u – 10v + 20v – 1 – 1 = 0


⇒ 10 v – 2 = 0



Put the value of v in (3) to get,



⇒ 10u – 2 – 1 = 0


⇒ 10u – 3= 0



Now



Hence speed of X and Y is .


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