Amanda is draining the water from two bathtubs. The table and graph below show the gallons of water remaining in each bathtub over time.

Question

Table of 'Bathtub A' shows in 0 minute 27 gallons, in 2 minutes 24 gallons, in 4 minutes 21 gallons and in 8 minutes 15 gallons of water remaining. Graph titled 'Bathtub B' shows points (0, 25) and (6, 17) are connected through a line.

Which bathtub will be empty first? Use the drop-down menus below to select the correct responses to complete the sentences.

Bathtub Query 1
will be empty first. The time it will take for this bathtub to be empty is Query 2
minutes.

Answer 1

To determine which bathtub will be empty first, we need to analyze the water remaining in both Bathtub A and Bathtub B over time.

For Bathtub A:

• At 0 minutes: 27 gallons remaining
• At 2 minutes: 24 gallons remaining
• At 4 minutes: 21 gallons remaining
• At 8 minutes: 15 gallons remaining

From the data, we see that Bathtub A decreases by 3 gallons every 2 minutes. To find when it will be empty, we can calculate:

• Current gallons: 27
• Decrease rate: 3 gallons every 2 minutes

To reach 0 gallons:

• 27 gallons ÷ 3 gallons/2 minutes = 18 minutes

So, Bathtub A will be empty in 18 minutes.

For Bathtub B: Using the graph, we can derive the rate of water drainage. The points provided are (0, 25) and (6, 17), meaning:

At 0 minutes: 25 gallons At 6 minutes: 17 gallons

Water drained in 6 minutes = 25 gallons - 17 gallons = 8 gallons

Rate: 8 gallons/6 minutes = 4/3 gallons per minute, or approximately 2.67 gallons per 2 minutes.

To find how long it will take for Bathtub B to drain from 25 gallons to 0 gallons:

• 25 gallons ÷ (4/3 gallons per minute) = 25 * (3/4) = 18.75 minutes.

Therefore, Bathtub B will be empty in 18.75 minutes.

Now, comparing the two:

1. Bathtub A will be empty first.
2. The time it will take for this bathtub to be empty is 18 minutes.

So the complete sentences would read:

Bathtub A will be empty first. The time it will take for this bathtub to be empty is 18 minutes.