SOLUTION: A large container is being filled with water at the rate of 2 3/4 gallons per minute. If the container leaks at the rate of 1/8 gallon a minute how long would it take to fill a 14

Algebra ->  Equations -> SOLUTION: A large container is being filled with water at the rate of 2 3/4 gallons per minute. If the container leaks at the rate of 1/8 gallon a minute how long would it take to fill a 14       Log On


   

Question 877095: A large container is being filled with water at the rate of 2 3/4 gallons per minute. If the container leaks at the rate of 1/8 gallon a minute how long would it take to fill a 14 gallon container? List all steps .
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1)
In words:
( rate of filling container ) x ( time to fill container )
minus
( rate of leaking from container ) x ( time to fill container )
equals
( the size of the container in gallons )
------------------------------------
(2)
Let +t+ = the time in minutes to fill
14 gallon container
--------------------
(3)
Convert 2 3/4 to quarters
2 3/4 = +11%2F4+
------------------
(4)
+%28+11%2F4+%29%2At+-+%28+1%2F8%29%2At+=+14+
Multiply both sides by +8+
+22t+-+t+=+112+
+21t+=+112+
+t+=+5.333+
----------------
(5)
Convert +1%2F3+ min to sec
+%281%2F3%29%2A60+=+20+
--------------------
It will take 5 min 20 sec to fill
the 14 gallon container
----------------------
(6)
check:
Convert +5.333+ to thirds
+5.333+=+16%2F3+
-----------------
+%28+11%2F4+%29%2At+-+%28+1%2F8%29%2At+=+14+
+%28+11%2F4+%29%2A%28+16%2F3+%29+-+%28+1%2F8%29%2A%28+16%2F3+%29+=+14+
Multiply both sides by +24+
+22%2A16+-+16+=+14%2A24+
+352+-+16+=+336+
+336+=+336+
OK