SOLUTION: Two pipes A and B fill a circular pond in 56 hour and 42hour respectively while a third pipe C can empty it in 72 hour .if all pipes are opened then what time will it takes to fill

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Two pipes A and B fill a circular pond in 56 hour and 42hour respectively while a third pipe C can empty it in 72 hour .if all pipes are opened then what time will it takes to fill      Log On


   

Question 924077: Two pipes A and B fill a circular pond in 56 hour and 42hour respectively while a third pipe C can empty it in 72 hour .if all pipes are opened then what time will it takes to fill the circular pound?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of filling, making the rate
of emptying negative
----------------------
Pipe A:
( 1 pond filled ) / 56 hrs
Pipe B:
( 1 pond filled ( / 42 hrs
Pipe C:
( 1 pond emptied ) / 72 hrs
--------------------------
Let +t+ = time in hrs to fill the pond
+1%2F56+%2B+1%2F42+-+1%2F72+=+1%2Ft+
+1+%2F+%28+7%2A8%29+%2B+1%2F%286%2A7%29+-+1%2F%289%2A8%29+=+1%2Ft+
Multiply both sides by +6%2A7%2A8%2A9%2At+
+6%2A9%2At+%2B+8%2A9%2At+-+6%2A7%2At+=+6%2A7%2A8%2A9+
Divide both sides by +3+
+18t+%2B+24t+-+14t+=+1008+
+28t+=+1008+
+t+=+36+
The pond will fill in 36 hrs
check:
I can use my calculator
+1%2F56+%2B+1%2F42+-+1%2F72+=+1%2F36+
+.017857+%2B+.023809+-+.013888+=+.027777+
+.027778+=+.027777+
close enough