document.write( "Question 404912: Working together, two people can mow a large lawn in 4 hours. One person can do the job alone 1 hour faster than the other person. How long does it take each person working alone to mow the lawn?\r
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Algebra.Com's Answer #286146 by ankor@dixie-net.com(22740)\"\" \"About 
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Working together, two people can mow a large lawn in 4 hours.
\n" ); document.write( " One person can do the job alone 1 hour faster than the other person.
\n" ); document.write( " How long does it take each person working alone to mow the lawn?
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\n" ); document.write( "let t = time required by the faster person
\n" ); document.write( "then
\n" ); document.write( "(t+1) = time required by the other person
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\n" ); document.write( "Let the completed job = 1
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\n" ); document.write( "each man will do a fraction of the work, the two fractions add up to 1
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\n" ); document.write( "\"4%2Ft\" + \"4%2F%28%28t%2B1%29%29\" = 1
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\n" ); document.write( "Multiply by t(t+1) to clear the denominators, results:
\n" ); document.write( "4(t+1) + 4t = t(t+1)
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\n" ); document.write( "4t + 4 + 4t = t^2 + t
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\n" ); document.write( "8t + 4 = t^2 + t
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\n" ); document.write( "0 = t^2 + t - 8t - 4
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\n" ); document.write( "t^2 - 7t - 4 = 0
\n" ); document.write( "we have to use the quadratic formula to solve this
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "In this problem x=t, a = 1, b= -7, c = -4
\n" ); document.write( "\"t+=+%28-%28-7%29+%2B-+sqrt%28-7%5E2-4%2A1%2A-4+%29%29%2F%282%2A1%29+\"
\n" ); document.write( "\"t+=+%28%2B7+%2B-+sqrt%2849+%2B+16+%29%29%2F2+\"
\n" ); document.write( "\"t+=+%28%2B7+%2B-+sqrt%2865+%29%29%2F2+\"
\n" ); document.write( "Two solutions, only want the positive solution
\n" ); document.write( "\"t+=+%28%2B7+%2B+8.06%29%2F2+\"
\n" ); document.write( "t = \"15.06%2F2\"
\n" ); document.write( "t = 7.53 hrs for the faster man to do the joy
\n" ); document.write( "and 8.53 hrs for the slower man
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\n" ); document.write( "Check solution
\n" ); document.write( "4/7.53 + 4/8.53
\n" ); document.write( "5.31 + .469 = 1; confirms our solutions of 7.53 and 8.53 hr \n" ); document.write( "
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