SOLUTION: 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 gi

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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? Can you solve the problem for me please with also showing me the way to do it
Found 2 solutions by ankor@dixie-net.com, richwmiller:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
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?
:
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
t = (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)
(45) = 9 mi
(45+9) = 9 mi
:
:
Did I make this understandable to you? C

Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
The other tutor makes it harder than it need be.
12x=10(x+9/60)
12x=10x+90/60
2x=90/60
x=45/60=45 minutes or 3/4 hour