Question

A commercial farm uses two water tanks as part of the irrigation system. The tanks are different sizes and drain at different rates.

After draining for 8 hours, tank A contains 70 gallons of water, and after 20 hours, the tank contains 64 gallons.
After draining for 10 hours, tank B contains 60 gallons of water, and after 30 hours, the tank contains 56 gallons.
After draining for how many hours will the two tanks contain the same amount of water, and what amount of water will remain in
each tank?
A. After draining for 47 hours, both tanks will have 68 gallons of water remaining.
B. After draining for 54 hours, both tanks will have 47 gallons of water remaining.
C. After draining for 40 hours, both tanks will have 54 gallons of water remaining.
D. After draining for 68 hours, both tanks will have 40 gallons of water remaining.

Answer 1

Option C; After draining for 40 hours, both tanks will have 54 gallons of water remaining.

Explanation:

Step 1; First we are required to find the rate at which tank A is losing water. The first tank after draining for 8 hours has 70 gallons remaining inside and in 20 hours contains 64 gallons. So in 12 hours (20 hours - 8 hours) tank A has lost 6 gallons. So tank A is losing 6 gallons in 12 hours which translates to tank A losing 0.5 gallons every hour.

Step 2; Secondly we find the rate at which tank B is losing water. The second tank after draining for 10 hours has 60 gallons and in 30 hours contains 56 gallons of water. So in 20 hours (30 hours - 10 hours) tank B has lost 4 gallons. So tank B is losing 4 gallons in 20 hours which translates to tank B losing 0.2 gallons every hour.

Step 3; Now we calculate how much water would be in the tanks after the different periods of time.

So for tank A at a rate of water draining 0.5 gallons per hour, there would be

54 gallons remaining in 40 hours, 50.5 gallons remaining in 47 hours, 47 gallons remaining in 54 hours and 40 gallons remaining in 68 hours.

For tank B at a rate of water draining 0.2 gallons per hour, there would be

54 gallons remaining in 40 hours, 52.6 gallons remaining in 47 hours, 51.2 gallons remaining in 54 hours and 48.4 gallons remaining in 68 hours.

So in 40 hours, both tank A and B will have 54 gallons of water in them. So option C is the answer.