Question 979260
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
:
{{{1/8.25}}}(t) = {{{1/9}}}(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 * {{{1/9}}} = 21{{{1/3}}} mi
176 * {{{1/8.25}}} = 21{{{1/3}}} mi