SOLUTION: A long distance runner starts at the beginning of a trail and runs at a rate of 6 miles per hour. An hour and a half later, a cyclist starts at the beginning of the trail and trave

Question 346616: A long distance runner starts at the beginning of a trail and runs at a rate of 6 miles per hour. An hour and a half later, a cyclist starts at the beginning of the trail and travels at a rate of 12 miles per hour. What is the amount of time that the cyclist travels before overtaking the runner?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A long distance runner starts at the beginning of a trail and runs at a rate of 6 miles per hour.
An hour and a half later, a cyclist starts at the beginning of the trail and
travels at a rate of 12 miles per hour.
What is the amount of time that the cyclist travels before overtaking the runner?
:
Let t = travel time of the cyclist
then
(t+1.5) = travel time of the runner (he start 1.5 hr before the cyclist)
:
When the cyclist overtakes the runner, they will have traveled the same distance
Write a distance equation: dist = speed * time
:
Cyclist dist = runner's dist
12t = 6(t+1.5)
12t = 6t + 9
12t - 6t = 9
3t = 9
t =
t = 3 hrs for the cyclist to catch the runner
:
:
We can confirm this solution by finding the actual distance each traveled;
(they should be equal)
12*3 = 27 mi
6(3+1.5) = 27 mi also
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