SOLUTION: Working​ together, two people can cut a large lawn in 5 hr. One person can do the job alone in 1 hr less than the other. How long would it take the faster person to do the&#8

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Working​ together, two people can cut a large lawn in 5 hr. One person can do the job alone in 1 hr less than the other. How long would it take the faster person to do the&#8      Log On

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Question 1111474: Working​ together, two people can cut a large lawn in 5 hr. One person can do the job alone in 1 hr less than the other. How long would it take the faster person to do the​ job?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Rate for 2 people is
[ 1 lawn ] / [ 5 hrs ]
Let +t+ = time for slower
person to mow 1 lawn
Slower person's rate:
[ 1 lawn ] / [ t hrs ]
Faster person's rate:
[ 1 lawn ] / [ t - 1 hrs ]
--------------------------
+1%2Ft+%2B+1%2F+%28t-1%29+=+1%2F5+
Multiply both sides by +t%2A%28+t-1+%29%2A5+
+5%2A%28+t-1+%29+%2B+5t+=+t%2A%28+t-1+%29+
+5t+-+5+%2B+5t+=+t%5E2+-+t+
+t%5E2+-11t+=+-5+
Complete the square
+t%5E2+-+11t+%2B+%2811%2F2%29%5E2+=+-5+%2B+%2811%2F2%29%5E2+
+t%5E2+-+11t+%2B+121%2F4+=+-20%2F4+%2B+121%2F4+
+%28+t+-+11%2F2+%29%5E2+=+101%2F4+
+t+-+5.5+=+sqrt%28+25.25+%29+
+t+=+5.5+%2B+5.025+
+t+=+10.525%0D%0Aand%0D%0A%7B%7B%7B+t+-+1+=+9.525+
Faster one takes 9.525 hrs working alone
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check:
+1%2Ft+%2B+1%2F%28t-1%29+=+1%2F5+
+1%2F10.525+%2B+1%2F9.525+=+1%2F5+
+.095+%2B+.105+=+.2+
+.2+=+.2+
OK
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