Question

Jada walks up to a tank of water that can hold up to 15 gallons. When it is active, a drain empties water from the tank at a constant rate. When Jada first sees the tank, it contains 12 gallons of water. Five minutes later, the tank contains 10 gallons of water.

Type your answers in the blanks below.

At what rate is the amount of water in the tank changing? Use a signed number, and include the unit of measurement in your answer.


How many more minutes will it take for the tank to drain completely?

________minutes

How many minutes before Jada arrived was the water take completely full?

_________ minutes

Answer 1

A) -2/5 gal/min

B) 25 minutes

C) 7.5 minutes

Explanation:

A) We are told that the tank contains 12 gallons of water when Jada first sees it.

5 minutes later, it loses two gallons to become 10 gallons.

Thus, rate at which the amount of water in the tank changing = -2/5 gal/min

B) After 5 minutes it contains 10 gallons. Since it drains at 2/5 gal/min, let us say the time to finish draining all is x, thus;

2/5 • x = 10

x = 10 × 5/2

x = 25 minutes

C) When full, it can hold up to 15 gallons. This is 3 more than the 12 she saw when she arrived.

Thus;

2/5 • y = 3

y = 5 × 3/2

y = 7.5 minutes