Two cyclists start biking from a trails start 3 hours apart

Two cyclists start biking from a trail\'s start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?

Solution

d=rt
d=6t for the first cyclist.
d=10(t-3) for the second cyclist.
Because the distances are the same set the 2 equations equal.
6t=10(t-3)
6t=10t-30
6t-10t=-30
-4t=-30
t=30/4
t=7.5 hours after the first cyclist leaves.
7.5-3=4.5 hours after the second cyclist leaves.