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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.