Question

A group of college students are volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Jillian can paint a certain room in 14 hours. Mike can paint the same room in 3 hours. Write an equation that can be used to find how long it will take them working together to paint the room.

Answer 1

the thing to remember in doing these problems is
1) the whole job is 1. 1 job
2) the rate is 1 over number of hours needed.

so the equation here is
\[(\frac{1}{14}+\frac{1}{3})x=1\] or if you prefer
\[\frac{17}{42}x=1\] or even
\[17x=42\]

Answer 2

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