A herd of elephants on the savannah is moving in a straight line at 3 miles per hour, headed directly toward a biologist who has been tracking them. Meanwhile, the biologist is also driving toward them at 43 miles per hour. If they started out 5 miles apart, how long will it be before they encounter one another?

Question

If necessary, round your answer to the nearest minute.
hours and
minutes

Answer 1

To determine how long it will be before the biologist and the herd of elephants encounter one another, we first need to calculate their relative speed, as they are moving towards each other.

1. Determine the speeds:

   • Speed of the elephants: 3 miles per hour
   • Speed of the biologist: 43 miles per hour

2. Calculate the relative speed: \[ \text{Relative speed} = \text{Speed of biologist} + \text{Speed of elephants} = 43 \text{ mph} + 3 \text{ mph} = 46 \text{ mph} \]

3. Initial distance:

   • They are 5 miles apart.

4. Time until encounter: Using the formula \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \): \[ \text{Time} = \frac{5 \text{ miles}}{46 \text{ mph}} \approx 0.1087 \text{ hours} \]

5. Convert hours to minutes: \[ 0.1087 \text{ hours} \times 60 \text{ minutes/hour} \approx 6.52 \text{ minutes} \]

6. Rounding to the nearest minute: The time until they encounter one another is approximately \( 7 \) minutes.

Thus, the time until the biologist encounters the herd of elephants is about 0 hours and 7 minutes.