Question

A takes 4hours more than B in walking 30 km. If A doubles his speed, he will take 1hr less than B. Find the speeds of A and B.

Answer 1

Distance = 30 km.
Let the speed of A be x km/hr.
And, the speed of B be y km/hr.

Then, time taken by A = `(30/x)"hrs"`.

Also, time taken by B = `(30/y)"hrs"`. 

As per given question, A takes 4hours more than B in walking 30 km.

⇒ `(30/x) = 4 + (30/y)`---(1)

Also, if A doubles his speed, he will take 1hr less than B.

⇒ `((30)/(2x)) + 1 =  (30/y)`---(2)

Using (2) in (1), gives:

`(30/x) = 4 + ((30)/(2x)) + 1`

⇒ `(30/x) - (15/x)` = 5

⇒ `(15)/x` = 5
⇒ x = 3km/hr.
From (1),

⇒ `(30/3) = 4 + (30/y)`

⇒ 6 = `(30/y)`
⇒ y = 5km/hr.
Thus, the speed of A is 3km/hr.
And, the speed of B is 5km/hr.