Question

Traveling at a speed of 12 mph, Jen biked home in 20 minutes. What was Jim's speed if he biked the same distance in 15 minutes?

Answer 1

To find Jim's speed, we first need to determine the distance that Jen biked home.

Jen's speed is 12 mph, and she took 20 minutes to bike home. First, we convert 20 minutes into hours:

\[
20 \text{ minutes} = \frac{20}{60} \text{ hours} = \frac{1}{3} \text{ hours}
\]

Next, we can calculate the distance Jen biked using the formula:

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

Substituting Jen's speed and time into the formula, we get:

\[
\text{Distance} = 12 \text{ mph} \times \frac{1}{3} \text{ hours} = 4 \text{ miles}
\]

Now that we know the distance Jen biked (4 miles), we can find Jim's speed. Jim biked the same distance in 15 minutes. We will also convert 15 minutes into hours:

\[
15 \text{ minutes} = \frac{15}{60} \text{ hours} = \frac{1}{4} \text{ hours}
\]

Now, we can calculate Jim's speed using the same distance and the time he took:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{4 \text{ miles}}{\frac{1}{4} \text{ hours}}
\]

To divide by a fraction, we multiply by its reciprocal:

\[
\text{Speed} = 4 \text{ miles} \times 4 = 16 \text{ mph}
\]

Therefore, Jim's speed was \( \boxed{16} \) mph.