SOLUTION: Company A is known to take 4 days longer than Company B to install the plumbing in a particular style of house. Using both companies together, it takes 5 days to install the plumb

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Company A is known to take 4 days longer than Company B to install the plumbing in a particular style of house. Using both companies together, it takes 5 days to install the plumb      Log On


   

Question 1114450: Company A is known to take 4 days longer than Company B to install the plumbing in a particular style of house. Using both companies together, it takes 5 days to install the plumbing. How long would it take each company alone to install the plumbing?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in days for company B
to install the plumbing
+t+%2B+4+ = time in days for company A
to install the plumbing
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The rate of working for both companies together:
[ 1 plumbing job ] / [ 5 days ]
Add rates for A and B to get rate working together
+1%2F%28t%2B4%29+%2B+1%2Ft+=+1%2F5+
Multiply both sides by +5t%2A%28+t%2B4+%29+
+5t+%2B+5%2A%28+t%2B4+%29+=+t%2A%28+t%2B4+%29+
+5t+%2B+5t+%2B+20+=+t%5E2+%2B+4t+
+t%5E2+-+6t+=+20+
Complete the square
+t%5E2+-+6t+%2B+9+=+20+%2B+9+
+%28+t+-+3+%29%5E2+=+%28+sqrt%2829+%29%29%5E2+
+t+-+3+=+sqrt%28+29+%29+
+t+=+3+%2B+5.385+
+t+=+8.385+
+t+%2B+4+=+12.385+
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Company A takes 12.385 days
Company B takes 8.385 days
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check:
+1%2F12.385+%2B+1%2F8.385+=+1%2F5+
+.08074+%2B+.11926+=+.2+
+.2+=+.2+
OK