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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.