SOLUTION: Two pipes can fill a tank is 34 minutes if both are turned on. If only one is used, it would take 36 minutes longers for the smaller pipe to fill the tank than the larder pipe. HO

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Two pipes can fill a tank is 34 minutes if both are turned on. If only one is used, it would take 36 minutes longers for the smaller pipe to fill the tank than the larder pipe. HO      Log On


   

Question 690312: Two pipes can fill a tank is 34 minutes if both are turned on. If only one is used, it would take 36 minutes longers for the smaller pipe to fill the tank than the larder pipe. HOw long will it take for the smaller pipe to fill the tank. (round to the nearest tenth if needed.)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = the time in minutes for the larger pipe to fill tank
+t+%2B+36+ = the time in minutes for the smaller pipe to fill tank
add their rates of filling to get the rate filling together
+1%2Ft+%2B+1%2F%28+t%2B36+%29+=+1%2F34+
Multiply both sides by +34t%2A%28+t%2B36+%29+
+34%2A%28+t%2B36+%29+%2B+34t+=+t%2A%28+t%2B36+%29+
+34t+%2B+1224+%2B+34t+=+t%5E2+%2B+36t+
+t%5E2+%2B+36t+-+68t+-+1224+=+0+
+t%5E2+-+32t+=+1224++
I can complete the square
+t%5E2+-+32t+%2B+%2832%2F2%29%5E2+=+1224+%2B+%2832%2F2%29%5E2++
+t%5E2+-+32t+%2B+256+=+1224+%2B+256+
+%28+t+-+16+%29%5E2+=+1480+ ( ignore negative square root of 1480 )
take the square root of both sides
+t+-+16+=+38.471+
+t+=+54.471+
+t+%2B+36+=+90.471+
It will take the smaller tank 90.5 min
or 1 hr 30 min and 30 sec
check:
+1%2Ft+%2B+1%2F%28+t%2B36+%29+=+1%2F34+
+1%2F54.471+%2B+1%2F90.471+=+1%2F34+
+.018358+%2B+.011053+=+.029412+
+.029411+=+.029412+
close enough