Question

Rita takes one hour longer than sita to walk 30km. but if Rita doubles her pace of walking she would be ahead of sita by 2 hrs . find the speed at which Rita and sita are walking

Answer 1

The speed of rita and sita are xkm/hr and ykm/hr respectively.
Rita covers xkm in 1hr
∴, rita covers 1km in 1/x hr
∴, rita covers 30km in 30/x hrs.
Similarly, sita covers 30 kim in 30/y hrs. Then by the given condition,
30/x-30/y=1
or, 30/y=30/x-1 -------------------(1)
Now, if rita doubled her speed i.e., 2x/hr then she will cover 30km in 30/2x=15/x hrs. Then by the given condition,
30/y-15/x=2
or, 30/x-1-15/x=2 [using (1)]
or, 30/x-15/x=2+1
or, 15/x=3
or, 1/x=3/15
or, 1/x=1/5
or, x=5km/hr
Putting in (1),
30/y=30/5-1
or, 30/y=6-1
or, 30/y=5
or, 1/y=5/30
or, 1/y=1/6
or, y=6km/hr
Speed of rita and sita are 5km/hr and 6km/hr respectively. Ans.