The water tank contains 12.3 gallons of water. Mark will fill the tank at a rate of 1.6 gallons per minute. The lake has 98.6 gallons of water and is being drained at a rate of 0.4 gallons per minute.
How many minutes will it take for the lake and the tank to contain the same amount of water

It will take 43.15 minutes for the lake and the tank to contain the same amount of water.

Step-by-step explanation:

Given that:

Water tank contains 12.3 gallons of water.

1.6 gallons per minute are being added by Mark.

Let,

m be the minutes in which water tank is filling.

T(m) = 1.6m + 12.3

The lake has 98.6 gallons of water.

Water is drained at a rate of 0.4 gallons per minute.

L(m) = -0.4m + 98.6

For same amount of water,

T(m) = L(m)

1.6m+12.3 = -0.4m+98.6

1.6m+0.4m = 98.6 -12.3

2.0m = 86.3

Dividing both sides by 2

Hence,

It will take 43.15 minutes for the lake and the tank to contain the same amount of water.