SOLUTION: Bill and Will are brothers who are both taking graduate level art classes. To help pay off their student loans, they decide to sell watercolor replicas of Andy Warhol's art. To pro

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Question 1126374: Bill and Will are brothers who are both taking graduate level art classes. To help pay off their student loans, they decide to sell watercolor replicas of Andy Warhol's art. To produce one piece of work, Bill takes 0.25 hours less than Will. Working together, it takes them 4 hours. Find the time it would take each of them if they worked individually. Round your answers to 2 decimal places.
Found 3 solutions by josmiceli, josgarithmetic, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = hrs that Will takes
+t+-+.25+ = hrs that Bill takes
add their individual rates to get their rate together
+1%2Ft+%2B+1%2F%28+t-.25+%29+=+1%2F4+
multiply both sides by +4t%2A%28+t-.25+%29+
+4%2A%28+t+-+.25+%29+%2B+4t+=+t%2A%28+t+-+.25+%29+
+4t+-+1+%2B+4t+=+t%5E2+-+.25t+
+t%5E2+-+8.25t+%2B+1+=+0+
+t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+t+=+%28-%28-8.25%29+%2B-+sqrt%28+%28-8.25%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29+
+t+=+%28+8.25+%2B-+sqrt%28+68.0625+-+4+%29%29%2F2+
+t+=+%28+8.25+%2B+8.004+%29%2F2+
+t+=+8.127+
and
+t+=+8.127+-+.25+
+t+=+7.877+
Will takes 8.13 hrs
Bill takes 7.88 hrs
-----------------------
check:
+1%2F8.13+%2B+1%2F7.88+=+1%2F4+
+.123+%2B+.127+=+.25+
+.25+=+.25+
OK
get a 2nd opinion if needed

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
           Rate in piece per hour

Bill      1%2F%28t-1%2F4%29

Will      1%2Ft

Together  1%2F4

Together rate is the sum of their individual rates.
1%2F%28t-1%2F4%29%2B1%2Ft=1%2F4

4t%28t-1%2F4%29%281%2F%28t-1%2F4%29%2B1%2Ft%29=4t%28t-1%2F4%29%281%2F4%29

4t%2B4%28t-1%2F4%29=t%28t-1%2F4%29

8t-1=t%5E2-t%2F4

32t-4=4t%5E2-t

highlight_green%284t%5E2-33t%2B4=0%29

Using general solution for quadratic equation,
t=%2833%2B-+sqrt%281025%29%29%2F8

The PLUS-form is necessary.

highlight%28t=%2833%2Bsqrt%281025%29%29%2F8%29------the time for Will alone.
Use this to find the time for Bill alone.

Answer by ikleyn(52781) About Me  (Show Source):