# How far should Sanya ride the bike for both to arrive home at the same time?

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Rohan and Sanya were out for a bike ride when the tyre on Rohan's bike burst.
They were 20 km from home, so they decided Rohan would walk back while Sanya would take the working bike, leave it further along the road and walk the rest of the way.
When Rohan reached the bike, he would ride it home.
If Rohan walks at 5 km/hr and rides at 12 km/hr and Sanya walks at 4 km/hr and rides at 10 km/hr, how far should Sanya ride the bike for both to arrive home at the same time?

posted Oct 4, 2018

Sanya should bike 12.5 km
.
For each hr Rohan walks Sanya will be 10-5 = 5 km faster.
For each hr Sanya walks Rohan will be 12-4 = 8 km faster,
Thus Sanya should bike 5/8 of the distance = 12.5 km and Rohan the remaining 3/8 = 7.5 km
.
Sanya will bike for 12.5/10 = 1.25 hr and walk for 7.5/4 = 1.875 hr for a total of 3.125 hr
Rohan will bike for 7.5/12 = 0.625 hr and walk for 12.5/5 = 2.5 hr for a total of 3.125 hr.

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