Two fish tanks, with 12 gallons & 3 gallons of water. The first fish tank is filled at rate of 1/3 gallons/minute and the other at a rate #1 ½# of the first. After how much time will both have equal amount of water if hoses are turned on simultaneously?

2 Answers
Jun 8, 2017

The rate of filling the 1st tank #1/3# gallon/min

The rate of filling the 2nd tank #1 1/2 of1/3=3/2of1/3=1/2# gallon/min

Let after t min the two tanks have equal amount of water,if hoses are turned on simultaneously. Initially two fish tanks, with 12 gallons & 3 gallons of water respectively.

So by the problem

#3+t/2=12+t/3#

#=>t/2-t/3=12-3#

#=>(3t-2t)/6=9#

#=>t/6=9#

#=>t=9xx6=54min#

Jun 8, 2017

Answer:

After #54# minutes both tanks will have same amount of water.

Explanation:

Let #t# be time in minutes after which both tanks will have same amount of water.
Rate of filling water in first tank is # 1/3# gallons per minute.
Rate of filling water in second tank is # 1 1/2*1/3 =cancel3/2*1/cancel3=1/2# gallons per minute.

By given condition , #12 +1/3t = 3+1/2t or 1/2t-1/3t=12-3 # or

#1/6t=9 or t=6*9=54# minutes.

After #54# minutes both tanks will have same amount of water.[Ans]