Question
Jack can swim 1/4 miles in 6/4 hours. How many miles can he swim in one hour?
16
14
64
12
16
14
64
12
Answers
GPT-4o mini
To find out how many miles Jack can swim in one hour, we first determine his swimming speed based on the information given.
Jack swims \( \frac{1}{4} \) miles in \( \frac{6}{4} \) hours, which simplifies to \( 1.5 \) hours.
Now, to find the speed in miles per hour, we use the formula:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]
Substituting Jack's distance and time:
\[
\text{Speed} = \frac{\frac{1}{4} \text{ miles}}{\frac{6}{4} \text{ hours}} = \frac{1/4}{1.5}
\]
To simplify this division:
\[
\text{Speed} = \frac{1}{4} \div \frac{6}{4} = \frac{1}{4} \times \frac{4}{6} = \frac{1}{6} \text{ miles per hour}
\]
Next, to find how far Jack can swim in one hour, we can set up the following:
\[
\text{Distance in 1 hour} = \text{Speed} \times 1 \text{ hour} = \frac{1}{6} \text{ miles}
\]
We realize there might be an error in the options given, as none of the calculated values from the provided options (16, 14, 64, 12) correspond to Jack's swimming distance, which is \( \frac{1}{6} \text{ miles} \).
Thus Jack swims \( \frac{1}{6} \) miles in one hour, confirming that none of the given options are correct.
Jack swims \( \frac{1}{4} \) miles in \( \frac{6}{4} \) hours, which simplifies to \( 1.5 \) hours.
Now, to find the speed in miles per hour, we use the formula:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]
Substituting Jack's distance and time:
\[
\text{Speed} = \frac{\frac{1}{4} \text{ miles}}{\frac{6}{4} \text{ hours}} = \frac{1/4}{1.5}
\]
To simplify this division:
\[
\text{Speed} = \frac{1}{4} \div \frac{6}{4} = \frac{1}{4} \times \frac{4}{6} = \frac{1}{6} \text{ miles per hour}
\]
Next, to find how far Jack can swim in one hour, we can set up the following:
\[
\text{Distance in 1 hour} = \text{Speed} \times 1 \text{ hour} = \frac{1}{6} \text{ miles}
\]
We realize there might be an error in the options given, as none of the calculated values from the provided options (16, 14, 64, 12) correspond to Jack's swimming distance, which is \( \frac{1}{6} \text{ miles} \).
Thus Jack swims \( \frac{1}{6} \) miles in one hour, confirming that none of the given options are correct.