Question

X takes 3 hours more than Y to walk 30 km. But, if X doubles his pace, he is ahead of Y by `1 1/2` hours. Find their speed of walking.

Answer 1

Let X and Y have speeds of x and y kilometres per hour, respectively.

Then, Time taken by X to travel 30 km = `30/x`

And time taken by Y to travel 30 km = `30/y`

According to the question,

`30/x = 30/y + 3`

⇒ `30/x - 30/y` = 3

⇒ `3(10/x - 10/y)` = 3

`10/x - 10/y` = 1  .......(i)

If X doubles his speed, then X's speed = 2x

Then, according to the question,

`30/y - 30/(2x) = 1 1/2`

`30/y - 15/x = 3/2`

⇒ `3(10/y - 5/x) = 3/2`

⇒ `20/y - 10/x` = 1  ...(ii)

Let `1/x` = p and `1/y` = q.

The equations then become

10p – 10q = 1   ......(iii)

And 20q – 10p = 1  ......(iv)

Adding equation (iii) and (iv}, we get

10q = 2

⇒ q = `2/10 = 1/5`

Putting q = `1/5` in equation (iii}, we get

`10p - 10 xx 1/5` = 1

⇒ 10p – 2 = 1

⇒ 10p = 1 + 2 = 3

⇒ p = `3/10`

Now, p = `1/x`

⇒ `3/10 = 1/x`

⇒ x = `10/3 = 3 1/3`

And q = `1/y`

⇒ `1/5 = 1/y`

⇒ y = 5

Hence, X's speed = `3 1/3` km/h and Y's speed= 5 km/h.