SOLUTION: working alone, Carrie can paint a house in three hours less than water. Together Carrie and Walter can paint to house in eight hours. How long does it take Walter to paint a hous

Algebra ->  Formulas -> SOLUTION: working alone, Carrie can paint a house in three hours less than water. Together Carrie and Walter can paint to house in eight hours. How long does it take Walter to paint a hous      Log On


   

Question 1031853: working alone, Carrie can paint a house in three hours less than water. Together Carrie and Walter can paint to house in eight hours. How long does it take Walter to paint a house alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = Walter's time in hrs to paint
a house working alone
+t+-+3+ = Carrie's time in hrs to paint
a house working alone
-----------------------------------
Walter's rate of painting working alone:
[ 1 house painted ] / [ t hrs ]
Carrie's rate of painting working alone:
[ 1 house painted ] / [ t - 3 hrs ]
Their rate painting together:
[ 1 house painted ] / [ 8 hrs ]
--------------------------------
Add their rates of painting to get their
rate painting together
+1+%2F+t+%2B+1+%2F+%28+t-3+%29+=+1%2F8+
Multiply both sides by +8%2At%2A%28+t-3+%29+
+8%2A%28+t-3+%29+%2B+8t+=+t%2A%28+t-3+%29+
+8t+-+24+%2B+8t+=+t%5E2+-+3t+
+t%5E2+-+19t+%2B+24+=+0+
Use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-19+
+c+=+24+
+t+=+%28-%28-19%29+%2B-+sqrt%28+%28-19%29%5E2+-+4%2A1%2A24+%29%29+%2F+%282%2A1%29+
+t+=+%28+19+%2B-+sqrt%28+361+-+96+%29%29+%2F+2+
+t+=+%28+19+%2B-+sqrt%28+265+%29%29+%2F+2+
+t+=+%28+19+%2B+16.279+%29+%2F+2+
+t+=+35.279%2F2+
+t+=+17.64+
and
+t+-+3+=+14.64+
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Walter can paint a house alone in 17.64
------------------
check:
+1+%2F+t+%2B+1+%2F+%28+t-3+%29+=+1%2F8+
+1%2F17.64+%2B+1%2F14.64+=+1%2F8+
+.0567+%2B+.0683+=+.125+
+.125+=+.125+
OK