Question

A car travels 75 miles in 3 hours. How far would it travel in 5 hours?



Solution

Let us represent the quantities as time (t) and distance (d).

Let us find the constant of proportionality between distance and time.

Value: 1


Identify the constant of proportionality.

a.
1/25

b.
25

c.
50

Answer 1

To find the constant of proportionality between distance and time, we can first calculate the speed of the car.

The formula for speed (which is the constant of proportionality in this case) is:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]

In this scenario:

- Distance = 75 miles
- Time = 3 hours

Now, substitute the values into the formula:

\[
\text{Speed} = \frac{75 \text{ miles}}{3 \text{ hours}} = 25 \text{ miles per hour}
\]

The constant of proportionality (the speed) is 25 miles per hour.

Now, let’s identify the constant of proportionality from the given options:

a. 1/25

b. 25

c. 50

The correct answer is **b. 25**.

Now, to determine how far the car would travel in 5 hours, we can use the speed we just calculated:

\[
\text{Distance} = \text{Speed} \times \text{Time}
\]

Substituting the values:

\[
\text{Distance} = 25 \text{ miles/hour} \times 5 \text{ hours} = 125 \text{ miles}
\]

Thus, the car would travel **125 miles** in 5 hours.