Question

Suman takes 3 hrs more than rashmi in walking.If suman doubles her speed,she will take 2 hrs less than Rashmi.If speed of rashmi is 1.5 km/hr.Find the speed of Rashmi and Suman ?

Answer 1

Speed of Rashmi is `1.5` km/hr. and speed of Suman is `1.05` km/hr.

Explanation:

The distance has not been given. Let us assume it `d` km.

Hence as speed of Rashmi is `1.5` km/hr., she will take `d/1.5` hours to cover the distance.

Let the speed of Suman be `x` km/hr. Suman takes `3` hrs. more than Rashmi. So she takes `3+d/1.5` hours. This means

`x xx (3+d/1.5)=d`

or `x=d/(3+d/1.5)=(3d)/(9+2d)` ...............(A)
(we have multiplied numerator and denominator in RHS by `3`)

If Suman doubles her speed it becomes `2x` and she takes `d/1.5-2` hours as she takes `2` hrs. less than Rashmi and hence

`2x xx(d/1.5-2)=d`

or `x=d/(2(d/1.5-2))=(3d)/(4d-12)` ...............(B)
(we have multiplied numerator and denominator in RHS by `3`)

From (A) and (B), we get

`(3d)/(9+2d)=(3d)/(4d-12)`

or `9+2d=4d-12`

i.e. `4d-2d=12+9`

or `2d=21`

i.e. `d=10.5`

Hence, speed of Suman is `(3xx10.5)/(9+2xx10.5)=31.5/30=1.05` km/hr.