Question

The amount of water in a bathtub that is getting filled at a constant rate is shown in the the table below.

Time Since Turning
on Faucet Amount of Water
3 seconds 375 milliliters
7 seconds 875 milliliters
9 seconds 1,125 milliliters
12 seconds ?
17 seconds 2,125 milliliters

What is the missing value in the table?

Answer 1

To determine the missing value in the table, we can analyze the pattern in the data provided.

From the information given:

- At 3 seconds, amount of water = 375 milliliters
- At 7 seconds, amount of water = 875 milliliters
- At 9 seconds, amount of water = 1,125 milliliters
- At 17 seconds, amount of water = 2,125 milliliters

Let's calculate the amount of water added for each time interval:

1. From 3 seconds to 7 seconds (4 seconds):
- Water added = 875 - 375 = 500 milliliters

2. From 7 seconds to 9 seconds (2 seconds):
- Water added = 1,125 - 875 = 250 milliliters

3. From 9 seconds to 17 seconds (8 seconds):
- Water added = 2,125 - 1,125 = 1,000 milliliters

Now, we can calculate the average rate of filling between the known values:

1. Between 3 and 7 seconds: 500 milliliters over 4 seconds gives us a rate of:
\[ \text{Rate} = \frac{500 \text{ ml}}{4 \text{ s}} = 125 \text{ ml/s} \]

2. Between 7 and 9 seconds: 250 milliliters over 2 seconds gives us a rate of:
\[ \text{Rate} = \frac{250 \text{ ml}}{2 \text{ s}} = 125 \text{ ml/s} \]

3. Between 9 and 17 seconds: 1,000 milliliters over 8 seconds gives us a rate of:
\[ \text{Rate} = \frac{1,000 \text{ ml}}{8 \text{ s}} = 125 \text{ ml/s} \]

The rate of filling appears to be consistent at 125 milliliters per second.

Now, let's determine the amount of water at 12 seconds:

- From 9 seconds to 12 seconds (3 seconds):
\[ \text{Water added} = 125 \text{ ml/s} \times 3 \text{ s} = 375 \text{ ml} \]

So, the amount of water at 12 seconds will be:
\[ 1,125 \text{ ml} + 375 \text{ ml} = 1,500 \text{ ml} \]

Therefore, the missing value in the table for the amount of water at 12 seconds is **1,500 milliliters**.