SOLUTION: One hose can fill a tank in 1.5 hours. Another hose can fill the same tank in .75 hours. How long will it take to fill the tank if both hoses are used?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: One hose can fill a tank in 1.5 hours. Another hose can fill the same tank in .75 hours. How long will it take to fill the tank if both hoses are used?      Log On


   

Question 1032090: One hose can fill a tank in 1.5 hours. Another hose can fill the same tank in .75 hours. How long will it take to fill the tank if both hoses are used?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of filling
Rate for 1st hose:
[ 1 tank filled ] / [ 1.5 hrs ]
Rate for 2nd hose:
[ 1 tank filled ] / [ .75 hrs ]
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Let +t+ = time in hrs to fill
the tank with both hoses
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+1%2F1.5+%2B+1%2F.75+=+1%2Ft+
Multiply both sides by +1%2F4+
+1%2F6+%2B+1%2F3++=+1%2F%284t%29+
Multiply both sides by +12t+
+2t+%2B+4t+=+3+
+6t+=+3+
+t+=+1%2F2+
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It will take 1/2 hr to fill tank
with both hoses
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check:
+1%2F1.5+%2B+1%2F.75+=+1%2Ft+
+1%2F1.5+%2B+1%2F.75+=+1%2F.5+
+2%2F3+%2B+4%2F3+=+2+
+6%2F3+=+2+
+2+=+2+
OK