SOLUTION: Mike can run the mile in 6 minutes and Dan can run the mile in 9 minutes. If Mike gives Dan a headstart of 1 minute, how far from the start will Mike pass Dan? How long does it tak

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Question 199978This question is from textbook College Algebra
: Mike can run the mile in 6 minutes and Dan can run the mile in 9 minutes. If Mike gives Dan a headstart of 1 minute, how far from the start will Mike pass Dan? How long does it take? This question is from textbook College Algebra

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Mike can run the mile in 6 minutes and Dan can run the mile in 9 minutes.
If Mike gives Dan a head-start of 1 minute, how far from the start will Mike pass Dan?
How long does it take?
:
Let t = M's running time
then
(t+1) = D's running time
:
When M catches D, they will have run the same distance
Write a distance equation from this fact
1%2F6t = 1%2F9(t+1)
Multiply both side by 18
3t = 2(t+1)
3t = 2t + 2
3t - 2t = 2
t = 2 minutes for M to catch D
:
Dist:
1%2F6 * 2 = 1%2F3 mile
and
1%2F9 * 3 = 1%2F3 mile