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 ?

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Answer 1 · 2017-01-24T06:44:58

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

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.