SOLUTION: Coleen and Justin go out for a bicycle ride. They leave from the same place riding in opposite directions. Justin is riding 10 miles per hour faster than Coleen. After riding for 6

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Question 923995: Coleen and Justin go out for a bicycle ride. They leave from the same place riding in opposite directions. Justin is riding 10 miles per hour faster than Coleen. After riding for 6 hours, they are 180 miles apart from each other. At what speed was Justin riding?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Defining a variable (what I would write first):
C= Coleen's speed in miles per hour.

Reasoning (no need to write all this):
C%2B10= Justin's speed in miles per hour. (You may or may not =want to write that).
So, the distance between Coleen and Justin starts at zero,
and increases at a rate of speed_sum=C%2B%28C%2B10%29=2C%2B10=2%28C%2B5%29 miles per hour.
So, after 6 hours, the distance between them must have increased to 6 times the rate of increase above.

Writing an equation (what I would write next):
6%2A%28C%2B%28C%2B10%29%29=180

Solving:
6%2A%28C%2BC%2B10%29=180 (you can skip this line)
6%2A%282C%2B10%29=180
12C%2B60=180
12C=180-60
12C=120
C=120%2F12
C=10
c%2B10=10%2B10=highlight%2820%29 is Justin's speed in miles per hour.

NOTES:
There are many ways to get the the same answer.

If just a fast answer and no work is required,
I would think through
6%2Aspeed_sum=180
speed_sum=180%2F6=30
C%2BC%2B10=30
2C%2B10=30
2C=20
C=10
C%2B10=highlight%2820%29
and maybe would try to do it without even picking up a pen or pencil.

Your teacher may be partial to
x= Justin's speed in miles per hour.
y= Coleen's speed in miles per hour.
system%28x=y%2B10%2C6%28x%2By%29=180%29-->system%28y=x-10%2Cx%2By=30%29-->x%2B%28x-10%29=30-->2x-10=30-->2x=30%2B10-->2x=40-->x=40%2F2-->x=20