https://file.aiquickdraw.com/mathbot/file/1730390973091rv2s18je.jpg

To find the constant of proportionality in this situation, we need to determine the rate at which gasoline is pumped, which is given by the formula:

\[
\text{Constant of proportionality} = \frac{\text{Time (s)}}{\text{Gasoline (gal)}}
\]

This constant should be approximately the same across all data points if the rate is consistent. Let's calculate it for each pair in the table:

1. For 17 gallons:
   \[
   \frac{136 \, \text{s}}{17 \, \text{gal}} = 8 \, \text{s/gal}
   \]

2. For 12 gallons:
   \[
   \frac{96 \, \text{s}}{12 \, \text{gal}} = 8 \, \text{s/gal}
   \]

3. For 10.5 gallons:
   \[
   \frac{84 \, \text{s}}{10.5 \, \text{gal}} = 8 \, \text{s/gal}
   \]

4. For 9.25 gallons:
   \[
   \frac{74 \, \text{s}}{9.25 \, \text{gal}} = 8 \, \text{s/gal}
   \]

Since all calculations yield the same result, the constant of proportionality is **8 seconds per gallon**.

Would you like more details or have any questions?

### Additional Related Questions
1. How would the constant change if the time doubled for each gallon pumped?
2. What if the rate of pumping was not consistent across the values? How would we handle it?
3. How does this concept relate to the slope of a line in a linear graph?
4. Could we use this constant to predict the time for any other amount of gasoline?
5. If we reverse the units, what would the rate look like in gallons per second?

### Tip
In problems involving proportional relationships, setting up ratios consistently helps check for errors and verify proportionality.

The table shows the time it takes to pump gasoline based on the number of gallons pumped. What is the constant of proportionality for this situation?

Learn how to determine the constant of proportionality for gasoline pumping time using the relationship between time in seconds and gallons pumped. Understand the concept of proportionality through calculations using a table of values.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation