Question 894920
Renee and Betsy decide to have a 10 mile race.
 Renee can run an average speed of 12 miles per hour while Betsy can run at an average speed of 10 miles per hour.
 Renee decides to give Betsy a head start of 9 minutes.
 How many minutes will it take Renee to catch up with Betsy?
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Since we are dealing in minutes here, we want to have their speeds in mi/min
R: 12/60 = 1/5 mi/min
B: 10/60 = 1/6 mi/min
:
let t = the running time of Renee when she catches Betsy (in minutes)
then
(t+9) = running time of Betsy
:
When R catches B they will have run the same distance
write a distance equation; dist = speed * time
{{{1/5}}}t = {{{1/6}}}(t+9)
multiply both sides by 30, cancel the denominators and you have
6t = 5(t+9)
6t = 5t + 45
6t - 5t = 45
t = 45 min for R to catch B
:
;
We can confirm this find the actual distance when this occurs (should be equal)
 {{{1/5}}}(45) = 9 mi
 {{{1/6}}}(45+9) = 9 mi
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Did I make this understandable to you? C