SOLUTION: Working together, Dan and Leah an mow a lawn in one hour and twelve minutes. Working alone, Leah can mow the lawn in one hours less time than it would take Dan. Find the time it ta

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Working together, Dan and Leah an mow a lawn in one hour and twelve minutes. Working alone, Leah can mow the lawn in one hours less time than it would take Dan. Find the time it ta      Log On


   

Question 919778: Working together, Dan and Leah an mow a lawn in one hour and twelve minutes. Working alone, Leah can mow the lawn in one hours less time than it would take Dan. Find the time it takes each of them to mow the lawn working alone.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = Dan's time in hrs to mow lawn
+t+-+1+ = Leah's time in hrs to mow lawn
Note that +12+ min = +12%2F60+=+1%2F5+ hrs
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Add their rates of working to get
their rate working together
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+1%2Ft+%2B+1%2F%28%28+t-1+%29%29+=+1%2F%28%286%2F5%29%29+
+1%2Ft+%2B+1%2F%28%28+t-1+%29%29+=+5%2F6+
Multiply both sides by +6t%2A%28+t-1+%29+
+6%2A%28+t-1+%29+%2B+6t+=+5t%2A%28+t-1+%29+
+6t+-+6+%2B+6t+=5t%5E2+-+5t+
+5t%5E2+-+17t+%2B+6+=+0+
Use quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+5+
+b+=+-17+
+c+=+6+
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+t+=+%28+-%28-17%29+%2B-+sqrt%28+%28-17%29%5E2+-+4%2A5%2A6+%29%29+%2F+%282%2A5%29+
+t+=+%28+17+%2B-+sqrt%28+289+-+120+%29%29+%2F+10+
+t+=+%28+17+%2B-+sqrt%28+169+%29%29+%2F+10+
+t+=+%28+17+%2B+13+%29+%2F+10+
+t+=+30%2F10+
+t+=+3+
+t+-+1+=+2+
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Dan's time is 3 hrs to mow lawn
Leah's time is 2 hrs to mow lawn
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check:
+1%2Ft+%2B+1%2F%28%28+t-1+%29%29+=+5%2F6+
+1%2F3+%2B+1%2F2+=+5%2F6+
+2%2F6+%2B+3%2F6+=+5%2F6+
+5%2F6+=+5%2F6+
OK