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?

Algebra ->  Rate-of-work-word-problems -> 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?      Log On


   

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) About Me  (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 1%2F30%2B1%2F42.

Using the relation rate*time=jobs, to do ONE job, (fill 1 barrel), we have
%281%2F30%2B1%2F42%29%2At=1.

The number of minutes then for both of them doing this one job is
t=1%2F%281%2F30%2B1%2F42%29.


Just look at the rate and simplify that first:
r=%287%2B5%29%2F%282%2A3%2A5%2A7%29
r=12%2F72
r=1%2F6, 1 barrels in 6 minutes

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