SOLUTION: Shelly works 4 hours less then william, together they finish the work in 7 hours, how long does it take will to finish the work?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Shelly works 4 hours less then william, together they finish the work in 7 hours, how long does it take will to finish the work?      Log On


   

Question 631976: Shelly works 4 hours less then william, together they finish the work in 7 hours, how long does it take will to finish the work?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = William's time in hours to finish job
+t+-+4+ = Shelly's time in hours to finish job
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Add their rates of working to get their rate
working together
+1%2Ft+%2B+1%2F%28+t-4%29+=+1%2F7+
Multiply both sides by +7%2At%2A%28+t+-+4+%29+
+7%2A%28+t+-+4+%29+%2B+7t+=+t%2A%28+t+-+4+%29+
+7t+-+28+%2B+7t+=+t%5E2+-+4t+
+t%5E2+-+18t+%2B+28+=+0+
Use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-18+
+c+=+28+
+t+=+%28-%28-18%29+%2B-+sqrt%28+%28-18%29%5E2+-+4%2A1%2A28+%29%29+%2F+%282%2A1%29+
+t+=+%28+18+%2B-+sqrt%28+324+-+112+%29%29+%2F+2+
+t+=+%28+18+%2B-+sqrt%28+212+%29%29+%2F+2+
+t+=+%28+18+-+14.56+%29+%2F+2+
++t+=+3.44%2F2+
+t+=+1.72+
----------
+t+=+%28+18+%2B+14.56+%29+%2F+2+
+t+=+32.56+%2F+2+
+t+=+16.28+
William finishes the work alone in 16.28 hrs
or 16 hrs 17 min
check:
+1%2Ft+%2B+1%2F%28+t-4%29+=+1%2F7+
+1%2F16.28+%2B+1%2F%28+16.28-4%29+=+1%2F7+
+.061425+%2B+.081433+=+.142857+
+.142858+=+.142857+
close enough