SOLUTION: Two hoses are used to fill a water trough. The first hose can fill it in 20 minutes while the second hose needs only 16 minutes. If the second hose is used for the first 4 minutes

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Question 536726: Two hoses are used to fill a water trough. The first hose can fill it in 20 minutes while the second hose needs only 16 minutes. If the second hose is used for the first 4 minutes and then the first is also used, how long will the first hose be used?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What are their rates of filling the trough?
Hose 1: ( 1 trough ) / ( 20 min )
Hose 2: ( 1 trough ) / ( 16 min )
How much of the trough does hose 2 get
filled in the 1st 4 minutes?
+%281%2F16%29%2A4+=+1%2F4+
That means there is +3%2F4+ of the trough
left to be filled using both hoses
Let t = time to fill 3/4 of trough with both hoses
---------
Add their rates of filling to get the rate
with both filling
+1%2F20+%2B+1%2F16+=+%283%2F4%29%2Ft+
+1%2F20+%2B+1%2F16+=+3%2F%284t%29++
Multiply both sides by 4
+1%2F5+%2B+1%2F4+=+3%2Ft+
Multiply both sides by 20t
+4t+%2B+5t+=+60+
+9t+=+60+
+t+=+6.667+ min
+.667%2A60+=+40+ sec
The 1st hose will be used for 6 min and 40 sec
check answer:
+1%2F20+%2B+1%2F16+=+%283%2F4%29%2Ft+
+.05+%2B+.0625+=+.75%2F6.667+
+.1125+=+.75%2F6.667+
+.7500375+=+.75+ ( error is from rounding )
OK