SOLUTION: A homeowner estimates that it will take him 8 days to roof his house. A professional roofer estimates that he could roof the house in 5 days. How long will it take if the homeowner

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: A homeowner estimates that it will take him 8 days to roof his house. A professional roofer estimates that he could roof the house in 5 days. How long will it take if the homeowner      Log On


   

Question 1154635: A homeowner estimates that it will take him 8 days to roof his house. A professional roofer estimates that he could roof the house in 5 days. How long will it take if the homeowner helps the roofer?
Thank you!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Home owner's rate of working:
[ 1 house roofed ] / [ 8 days ]
Professional's rate of working:
[ 1 house roofed ] / [ 5 days ]
let their rate working together be:
[ 1 house roofed ] / [ t days ]
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Add their rates to get rate working together
+1%2F8+%2B+1%2F5+=+1%2Ft+
Multiply both sides by +40t+
+5t+%2B+8t+=+40+
+13t+=+40+
+t+=+3.077+
3.077 days
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check:
+1%2F8+%2B+1%2F5+=+1%2Ft+
+.125+%2B+.2+=+1%2F3.077+
+.325+=+.32499+
The error is due to rounding off