SOLUTION: Cara can pick enough apples to fill a barrel in half an hour. Jim takes 42 minutes to do it. In how many minutes can they pick a barrel full if they do it together?

Question 708075: Cara can pick enough apples to fill a barrel in half an hour. Jim takes 42 minutes to do it. In how many minutes can they pick a barrel full if they do it together?
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
If they work together, we are assuming their rates are additive.
Cara does 1 barrel in 30 minutes, rate is 1/30.
Jack's work rate is 1/42 barrels per minute.

Working together, their rate is .

Using the relation rate*time=jobs, to do ONE job, (fill 1 barrel), we have
.

The number of minutes then for both of them doing this one job is
.

Just look at the rate and simplify that first:

, 1 barrels in 6 minutes

Refer back a bit to , that job is done in 6 minutes.
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