document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #560600 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
Defining a variable (what I would write first):
\n" ); document.write( " $\"C\"$ = Coleen's speed in miles per hour.
\n" ); document.write( "
\n" ); document.write( "Reasoning (no need to write all this):
\n" ); document.write( " $\"C%2B10\"$ = Justin's speed in miles per hour. (You may or may not =want to write that).
\n" ); document.write( "So, the distance between Coleen and Justin starts at zero,
\n" ); document.write( "and increases at a rate of $\"speed_sum=C%2B%28C%2B10%29=2C%2B10=2%28C%2B5%29\"$ miles per hour.
\n" ); document.write( "So, after $\"6\"$ hours, the distance between them must have increased to $\"6\"$ times the rate of increase above.
\n" ); document.write( "
\n" ); document.write( "Writing an equation (what I would write next):
\n" ); document.write( " $\"6%2A%28C%2B%28C%2B10%29%29=180\"$
\n" ); document.write( "
\n" ); document.write( "Solving:
\n" ); document.write( " $\"6%2A%28C%2BC%2B10%29=180\"$ (you can skip this line)
\n" ); document.write( " $\"6%2A%282C%2B10%29=180\"$
\n" ); document.write( " $\"12C%2B60=180\"$
\n" ); document.write( " $\"12C=180-60\"$
\n" ); document.write( " $\"12C=120\"$
\n" ); document.write( " $\"C=120%2F12\"$
\n" ); document.write( " $\"C=10\"$
\n" ); document.write( " $\"c%2B10=10%2B10=highlight%2820%29\"$ is Justin's speed in miles per hour.
\n" ); document.write( "
\n" ); document.write( "NOTES:
\n" ); document.write( "There are many ways to get the the same answer.
\n" ); document.write( "
\n" ); document.write( "If just a fast answer and no work is required,
\n" ); document.write( "I would think through
\n" ); document.write( " $\"6%2Aspeed_sum=180\"$
\n" ); document.write( " $\"speed_sum=180%2F6=30\"$
\n" ); document.write( " $\"C%2BC%2B10=30\"$
\n" ); document.write( " $\"2C%2B10=30\"$
\n" ); document.write( " $\"2C=20\"$
\n" ); document.write( " $\"C=10\"$
\n" ); document.write( " $\"C%2B10=highlight%2820%29\"$
\n" ); document.write( "and maybe would try to do it without even picking up a pen or pencil.
\n" ); document.write( "
\n" ); document.write( "Your teacher may be partial to
\n" ); document.write( " $\"x\"$ = Justin's speed in miles per hour.
\n" ); document.write( " $\"y\"$ = Coleen's speed in miles per hour.
\n" ); document.write( " $\"system%28x=y%2B10%2C6%28x%2By%29=180%29\"$ --> $\"system%28y=x-10%2Cx%2By=30%29\"$ --> $\"x%2B%28x-10%29=30\"$ --> $\"2x-10=30\"$ --> $\"2x=30%2B10\"$ --> $\"2x=40\"$ --> $\"x=40%2F2\"$ --> $\"x=20\"$ \n" ); document.write( "

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