Question

A whale-watching tour boat has finished viewing a whale and is returning to shore, moving 44 miles per hour. The whale coincidentally starts swimming away from the boat at the same time, moving in the exact opposite direction at a rate of 19 miles per hour. How long will it be before the whale and the boat are 5 miles apart?
If necessary, round your answer to the nearest minute.
hours and
minutes

Answer 1

To find out how long it will take for the whale and the boat to be 5 miles apart, we can first determine their relative velocity since they are moving in opposite directions.

1. **Calculate the relative speed**:
- The boat is moving at 44 miles per hour.
- The whale is swimming at 19 miles per hour.
- Since they are moving in opposite directions, we add their speeds:
\[
\text{Relative speed} = 44 + 19 = 63 \text{ miles per hour}
\]

2. **Set up the equation to find time**:
We want to find out how much time \( t \) (in hours) it takes for them to be 5 miles apart. We can use the formula:
\[
\text{Distance} = \text{Relative Speed} \times t
\]
Rearranging this gives:
\[
t = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{5}{63}
\]

3. **Calculate the time**:
\[
t = \frac{5}{63} \text{ hours}
\]

4. **Convert hours to minutes**:
To convert hours into minutes, multiply by 60:
\[
t = \frac{5}{63} \times 60 \approx 4.76 \text{ minutes}
\]

5. **Round to the nearest minute**:
Rounding 4.76 to the nearest minute gives us approximately 5 minutes.

Thus, the answer is:
- **Time until they are 5 miles apart**: 0 hours and 5 minutes.