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

1st cyclist DATA:
rate = 6 mph ; time = t hrs. ; distance = 6t miles
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2nd cyclist DATA:
rate = 10 mph ; time = t-3 hrs ; distance = 10(t-3) miles
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How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?
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Equation:
distance = distance
6t = 10(t-3)
6t = 10t - 30
4t = 30
t = 7.5 hrs (time for cyclist # 1)
t-3 = 4.5 hrs (time for cyclist # 2)