# 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 ?

Jan 24, 2017

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 $\frac{d}{1.5}$ hours to cover the distance.

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

$x \times \left(3 + \frac{d}{1.5}\right) = d$

or $x = \frac{d}{3 + \frac{d}{1.5}} = \frac{3 d}{9 + 2 d}$ ...............(A)
(we have multiplied numerator and denominator in RHS by $3$)

If Suman doubles her speed it becomes $2 x$ and she takes $\frac{d}{1.5} - 2$ hours as she takes $2$ hrs. less than Rashmi and hence

$2 x \times \left(\frac{d}{1.5} - 2\right) = d$

or $x = \frac{d}{2 \left(\frac{d}{1.5} - 2\right)} = \frac{3 d}{4 d - 12}$ ...............(B)
(we have multiplied numerator and denominator in RHS by $3$)

From (A) and (B), we get

$\frac{3 d}{9 + 2 d} = \frac{3 d}{4 d - 12}$

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

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

or $2 d = 21$

i.e. $d = 10.5$

Hence, speed of Suman is $\frac{3 \times 10.5}{9 + 2 \times 10.5} = \frac{31.5}{30} = 1.05$ km/hr.