Work Rate problems

I don't understand how to set up and solve work rate problems, here's a sample problem

"Gina and Kayla start a business painting fences. They discover they can paint a fence in 40 minutes if they work together. Gina can paint the fence in 70 minutes if she works alone. How long would it take for Kayla to paint a fence by herself?"

Answers
A possible general approach is to decide what you would ideally like to know and then to pretend that you do know - by assigning a letter to that value. In this example you could let g = Gina's fence painting rate in fences per minute, and then k = Kayla's rate. Then look at the facts given and express then in terms of those facts. g = 1/70. The distance that gina or kayla can paint in a given time is the respective rate multiplied by the time, so in 40 mins gina can paint 40g fences. Kayla paints 40k of the fence. Between them they paint the whole fence so 40g + 40k = 1 We'll let you finish this off.
ianmoth
01 April 2013
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