SOLUTION: Janene and Emily plan to go on a marathon training run. Emily arrives late, so Janene starts running 16 minute before Emily. Janene runs at an average rate of 9 minutes per mile, a

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Question 979260: Janene and Emily plan to go on a marathon training run. Emily arrives late, so Janene starts running 16 minute before Emily. Janene runs at an average rate of 9 minutes per mile, and Emily runs at an average rate of 8 1/4 minute per mile. Assuming that both girls started at the same location and ran the same route, how many minutes will Emily take to catch up to Janene?
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Janene starts running 16 minute before Emily.
Janene runs at an average rate of 9 minutes per mile, and Emily runs at an average rate of 8 1/4 minute per mile.
Assuming that both girls started at the same location and ran the same route, how many minutes will Emily take to catch up to Janene?
:
Let t = time for E to catch J
then
(t+16) = running time for J when she is caught
:
The reciprocal allows us the change their speed to mi per min
1/9 mi/min is J's speed
1/8.25 mi/min is E's speed
:
When E catches J, they will have ran the same distance
Write a distance equation, dist = speed * time
:
(t) = (t+16)
multiply both sides by the product of 8.25 & 9, results:
9t = 8.25(t+16)
9t = 8.25t + 132
9t - 8.25t = 132
.75t = 132
t = 132/.75
t = 176 minutes for E to Catch J
:
:
Confirm this by finding the actual distances they ran, should be the same
J ran 16 + 176 = 192 min
192 * = 21 mi
176 * = 21 mi