Question

.
John and Caden are at the park playing basketball when John gets a text telling him to come home for dinner. He and Caden live on opposite ends of the park, so they head in opposite directions. John jogs due north at 6 feet per second. Caden walks due south at 4 feet per second. How long will it take for John and Caden to be 750 feet apart?
minutes and
seconds

Answer 1

To determine how long it will take for John and Caden to be 750 feet apart, we can sum their rates of movement because they are moving in opposite directions.

1. **John's speed**: 6 feet per second (north)
2. **Caden's speed**: 4 feet per second (south)

The combined speed of John and Caden moving apart is:
\[
6 \, \text{feet/second} + 4 \, \text{feet/second} = 10 \, \text{feet/second}
\]

Now, we want to find the time it will take for them to be 750 feet apart. We can use the formula:
\[
\text{distance} = \text{speed} \times \text{time}
\]
Rearranging this formula to find time gives us:
\[
\text{time} = \frac{\text{distance}}{\text{speed}}
\]

Plugging in the distances and speeds:
\[
\text{time} = \frac{750 \, \text{feet}}{10 \, \text{feet/second}} = 75 \, \text{seconds}
\]

To convert 75 seconds into minutes and seconds:
- There are 60 seconds in a minute, so divide 75 by 60.
\[
\text{minutes} = 1 \quad \text{and} \quad \text{seconds} = 75 - 60 = 15
\]

Thus, the time it will take for John and Caden to be 750 feet apart is:
**1 minute and 15 seconds.**