document.write( "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? \n" ); document.write( "
Algebra.Com's Answer #407274 by ptaylor(2198)\"\" \"About 
You can put this solution on YOUR website!
Let x=amount of time it takes Ev to do the dishes
\n" ); document.write( "Then Ev works at the rate of 1/x of the dishes per minute
\n" ); document.write( "It takes John x+5 minutes to do the dishes
\n" ); document.write( "Then John works at the rate of 1/(x+5) of the dishes per minute
\n" ); document.write( "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
\n" ); document.write( "So our equation to solve is:
\n" ); document.write( "1/x +1/(x+5)=1/20 multiply each term by 20x(x+5)
\n" ); document.write( "20(x+5)+20x=x(x+5) simplify
\n" ); document.write( "20x+100+20x-x^2+5x and this gives us
\n" ); document.write( "x^2-35x-100=0 quadratic in standard form --solve using quadratic formula
\n" ); document.write( " \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( " \"x+=+%2835+%2B-+sqrt%28+%28-35%29%5E2-4%2A%28-100%29%29%29%2F%282%29+\"
\n" ); document.write( "\"x+=+%2835+%2B-+sqrt%28+1225%2B400%29%29%2F%282%29+\"
\n" ); document.write( "\"x+=+%2835+%2B-+sqrt%28+1625%29%29%2F%282%29+\"
\n" ); document.write( "\"x+=+%2835+%2B-+40.3%29%2F%282%29+\"
\n" ); document.write( "\"x+=+%2835+%2B40.3%29%2F%282%29+\" and
\n" ); document.write( "\"x+=+%2835-40.3%29%2F%282%29+\"-----disregard--- this is a negative number
\n" ); document.write( "so we have:
\n" ); document.write( "x=37.65 min---amount of time it takes Ev to wash the dishes working alone
\n" ); document.write( "x+5=37.65+5=42.65 min --time it takes John working alone
\n" ); document.write( "CK
\n" ); document.write( "1/(37.65) + 1/(42.65)=1/20 I hope it does
\n" ); document.write( "Another way to check this problem:
\n" ); document.write( "20/(37.65) + 20/(42.65) should equal 1 (one set of dishes, that is)\r
\n" ); document.write( "\n" ); document.write( "Hope this helps--ptaylor\r
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