Question

Jake fills a tank that can hold 200 gallons of water. The tank already has 50 gallons of water in it when Jake starts filling it at the rate of 10 gallons per minute. Kala fills a tank that can hold 300 gallons of water. That tank already has 100 gallons of water in it when Karla starts filling it at the rate of 5 gallons per minute. Jake and Kala start filling the tanks at the same time. How long after they start filling the tanks do the tanks have the same volume of water? What is that volume of water?

A) 5 minutes, 150 gallons
B) 10 minutes, 150 gallons
C) 5 minutes, 250 gallons
D) 10 minutes, 250 gallons

Answer 1

After 10 minutes, both tanks will have the same volume of water, which is 150 gallons. The correct answer is B) 10 minutes, 150 gallons.

Step-by-step explanation:

To determine when the tanks have the same volume of water, we must calculate the volume in each tank after a certain time.

Jake starts with 50 gallons and adds water at a rate of 10 gallons per minute. Kala starts with 100 gallons and adds water at a rate of 5 gallons per minute. We are looking for the time t when the volumes are equal. Therefore, we can set up the following equation for equal volumes:

50 + 10t = 100 + 5t

Combining like terms, we have:

5t = 50

Dividing each side by 5 gives us:

t = 10

After 10 minutes they will have the same volume of water.

To find out what that volume is, we substitute t back into one of the original equations:

50 + 10(10) = 150 gallons

Therefore, the correct answer is B) 10 minutes, 150 gallons.