Question

Tank A contains 35 gallons of water and is increasing at a rate of 5 gallons per minute.

Tank B contains 100 gallons of water and is decreasing at a rate of 8 gallons per minute.



a) In how many minutes will the tanks contain the same amount of water?



b) How much water will that be?

Answer 1

a) Let's represent the amount of minutes as 't'.

In t minutes, the amount of water in Tank A will be 35 + 5t.
In t minutes, the amount of water in Tank B will be 100 - 8t.

To find when the tanks contain the same amount of water, we need to solve the equation:
35 + 5t = 100 - 8t

Adding 8t to both sides:
35 + 13t = 100

Subtracting 35 from both sides:
13t = 65

Dividing both sides by 13:
t = 5

Therefore, the tanks will contain the same amount of water in 5 minutes.

b) To find out how much water that would be, we can substitute t into either tank's equation. Let's use Tank A:
Amount of water in Tank A = 35 + 5t
Amount of water in Tank A = 35 + 5(5)
Amount of water in Tank A = 35 + 25
Amount of water in Tank A = 60

Therefore, the tanks will contain 60 gallons of water when they have the same amount.