# Cyclists Rate Problem--SET UP?!?!?

#### kemccla

##### New member
Two cyclists start biking from a trail 3 hrs. apart. The second cyclist travels at 10 mph and starts 3 hrs. after hte 1st cyclist who is travelling at 6 mph. How much time will pass before hte second cyclist catches up with the first from the time the second cyclist started biking?

The answer is 4.5 hrs. BUT how do you set this problem up to solve?!?!?!

#### arthur ohlsten

##### Full Member
distance first cycalist travels at time T,D1, when traveling at 6 mph at time
D1=6T

distance second cyclist travels in time [T-3],D2 at 10 mph
D2=[T-3]10

when are the distances the same?
D1=D2
6T=10[T-3]
6T=10T-30
30=4T
T=7.5 hours after first cyclist starts, or he will catch up in 4.5 hours

I suggest you do the problem another way!
the first cyclist is how far ahead at the time the second cyclist starts?
How fast is the second cyclist catching up to the first?
How long does it take to catch up?

Arthur

#### kemccla

##### New member
Thanks so much for the helpful reply!

you are welcome
Arthur