SOLUTION: A long distance runner starts at the beginning of a trail and runs at a rate of 6 miles per hour. Two hours later, a cyclist starts at the beginning of the trail and travels at a r

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Question 518430: A long distance runner starts at the beginning of a trail and runs at a rate of 6 miles per hour. Two hours later, a cyclist starts at the beginning of the trail and travels at a rate of 22 miles per hour. What is the amount of time that the cyclist travels before overtaking the runner?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A long distance runner starts at the beginning of a trail and runs at a rate of 6 miles per hour.
Two hours later, a cyclist starts at the beginning of the trail and travels at a rate of 22 miles per hour.
What is the amount of time that the cyclist travels before overtaking the runner?
:
let t = travel time of the bike
then
(t+2) = running time of the runner
:
When the bike overtakes the runner, they will have traveled the same distance
Write a distance equation; dist = speed * time
:
6(t+2) = 22t
6t + 12 = 22t
12 = 22t - 6t
12 = 16t
t = 12%2F16
t = .75 hrs, or 45 min for the bike to overtake the ground-pounder
:
:
Check by finding the actual dist of each, they should be equal
22(.75) = 16.5 mi
6(2.75) = 16.5 mi