SOLUTION: if john and ev do the dishes together, it takes them 20 minutes. It takes john 5 minutes longer than ev if he works alone. How long does it approximately take each of them working

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Question 650191: if john and ev do the dishes together, it takes them 20 minutes. It takes john 5 minutes longer than ev if he works alone. How long does it approximately take each of them working alone to do the dishes?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of time it takes Ev to do the dishes
Then Ev works at the rate of 1/x of the dishes per minute
It takes John x+5 minutes to do the dishes
Then John works at the rate of 1/(x+5) of the dishes per minute
Together they work at the rate of 1/x +1/(x+5) of the dishes per minute but we know that together they work at the rate of 1/20 of the dishes per minute
So our equation to solve is:
1/x +1/(x+5)=1/20 multiply each term by 20x(x+5)
20(x+5)+20x=x(x+5) simplify
20x+100+20x-x^2+5x and this gives us
x^2-35x-100=0 quadratic in standard form --solve using quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%2835+%2B-+sqrt%28+%28-35%29%5E2-4%2A%28-100%29%29%29%2F%282%29+
x+=+%2835+%2B-+sqrt%28+1225%2B400%29%29%2F%282%29+
x+=+%2835+%2B-+sqrt%28+1625%29%29%2F%282%29+
x+=+%2835+%2B-+40.3%29%2F%282%29+
x+=+%2835+%2B40.3%29%2F%282%29+ and
x+=+%2835-40.3%29%2F%282%29+-----disregard--- this is a negative number
so we have:
x=37.65 min---amount of time it takes Ev to wash the dishes working alone
x+5=37.65+5=42.65 min --time it takes John working alone
CK
1/(37.65) + 1/(42.65)=1/20 I hope it does
Another way to check this problem:
20/(37.65) + 20/(42.65) should equal 1 (one set of dishes, that is)
Hope this helps--ptaylor