How far away can a boy ride on a bicycle if he rides away at 10 kilometers per hour and returns at 9 kilometers per hour? The entire trip takes 9.5 hours.

Alright, so he went the same distance there and back, but at different speeds

hmm

d=st

d/s=t

total time is 9.5hr

alright

so distance there=distance back we will call both of them d

so

speed there is 10

speed back is 9

total time is 9.5

so

d/sthere+d/sback=totaltime

d/10+d/9=9.5

times both sides by 90

9d+10d=855

19d=855

divide both sides by 19

d=45

he can ride 45mi away