Question

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

Answer 1

X takes 3 hours more than Y to walk 30 km .

speed of X is x and speed of Y is y .

=> 30/x = 30/y +3

=> 30/x - 30/y = 3 -----------1

and , X doubles his pace, he is ahead of Y by 3/2 hours

=> 30 /2x + 3/2 = 30/y

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

let 1/x = a and 1/y = b ,

so , from 1 and 2 equation ,

30a - 30b = 3
- 15a - 30 b = -3/2
--------------------------------
15 a = 9/2

a = 9/30 = 3/10

and , b = (30×3/10 -3)/30 = 6/30= 1/5

now , 1/x = a = 3/10
so, x = 10/3 km/h

and = 1/y = b = 1/5
so , y = 5km/h

Answer 2

Detailed Solution :

             ↓

The question says that time taken by X is 3 hrs more than Y to complete a distance of 30 km.

So, if speed of X and Y are x km/h and y km/h respectively, then

⇒ 30/x = 3 + 30x/4

⇒ 30/x - 30/y = 3

⇒ 10/x - 10/y = 1

Taking 1/x as u and 1/y as v, we get

→ 10u - 10v = 1 ___(1)

Now, if X doubles it's speed means 2x km/h then he will complete distance 3/2 hrs before than Y.

⇒ 30/2x = 30/y - 3/2

⇒ 30/2x - 30/y = - 3/2

⇒ 10/2x - 10/y = - 1/2

⇒  10u/2 - 10v = - 1/2

→ 5u - 10v = - 1/2 ___(2)

By subtracting eq(1) by (2) we get,

⇒ 5u = 1 + 1/2

⇒ u = 3/10

Then, 10(3/10) - 10v = 1

⇒ - 10v = - 2

⇒ v = 1/5

Since 1/x = u and 1/y = v,

→ x = 10/3 km/h and y = 5 km/h

Hence speed of X is 10/3 km/h and Y = 5 km/h.