Question

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?

Answer 1

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`

Answer 2

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]