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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 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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