SOLUTION: Butch starts peeling potatoes at the rate of 3 potatoes per minute. Four minutes later Janet joins him and peels at the rate of 5 potatoes per minute. Eventually Janet catches up

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Question 857431: Butch starts peeling potatoes at the rate of 3 potatoes per minute. Four minutes later Janet joins him and peels at the rate of 5 potatoes per minute. Eventually Janet catches up to Butch. The equation below can be used to model this situation, where x represents the amount of time in minutes that Butch has been peeling.
3x=5(x-4)
How many potatoes has Butch peeled when Janet catches up?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Uniform Rates, work of peeling potatos.
R*T=P for rate in potatos per minute, time in minutes, potato count peeled.
Let t = amount of time for Janet to catchup with Butch, or the time that both have peeled the same number of potatos.
Let p = amount of potatos each person has peeled, WHEN EACH HAS DONE THE SAME NUMBER OF THEM.

_____________rate_________time_________Potatos Count
Butch________3____________t+4__________p
Janet________5____________t____________p

The rate equation gives us these two equations:
Butch: p=3(t+4)
Janet: p=5t

You used x, while I used t. same meaning. Your point of view of time is a little different but no matter. Janet's time is 4 minutes less than Butch; Butches time is 4 minutes more than Janet's.

The two expression for p are equal.
highlight_green%283%28t%2B4%29=5t%29
3t%2B12=5t
12=5t-3t
2t=12
highlight%28t=6%29 minutes for Janet to catch up with Butch, meaning when they both peeled the same number of potatos.