SOLUTION: A bathtub can be filled by the cold water faucet in 5 minutes and by the hot water faucet in 20 minutes. How long does it take to fill the tub if both faucets are open?

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Question 1055877: A bathtub can be filled by the cold water faucet in 5 minutes and by the hot water faucet in 20 minutes. How long does it take to fill the tub if both faucets are open?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add the rates of filling
For the cold water faucet:
rate of filling = [ 1 bathtub filled ] / [ 5 min ]
For the hot water faucet:
rate of filling = [ 1 bathtub filled ] / [ 20 min ]
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Let +t+ = time in minutes to fill tub with both
faucets open
+1%2F5+%2B+1%2F20+=+1%2Ft+
Multiply both sides by +20t+
+4t+%2B+t+=+20+
+5t+=+20+
+t+=+4+
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With both faucets open the tub is filled in 4 min
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check:
+4%2F20+%2B+1%2F20+=+1%2Ft+
+4%2F20+%2B+1%2F20+=+1%2F4+
+5%2F20+=+5%2F20+
OK