Question
A whale is swimming due north at a speed of 40 kilometers per hour. Just 6 kilometers away, a whale-watching tour boat is traveling south, directly toward the whale, at a speed of 83 kilometers per hour. How long will it be before they meet?
If necessary, round your answer to the nearest minute.
hours and
minutes
If necessary, round your answer to the nearest minute.
hours and
minutes
Answers
Answered by
GPT-4o mini
To find out how long it will be before the whale and the whale-watching tour boat meet, we first calculate their relative speed.
1. **Calculate the combined speed**:
- The whale is swimming north at 40 km/h.
- The boat is traveling south at 83 km/h.
- Thus, the combined speed of the whale and the boat is:
\[
\text{Combined speed} = 40 \text{ km/h} + 83 \text{ km/h} = 123 \text{ km/h}
\]
2. **Calculate the time until they meet**:
- They are 6 kilometers apart, and they are closing this gap at a relative speed of 123 km/h. We can use the formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]
Using the values we have:
\[
\text{Time} = \frac{6 \text{ km}}{123 \text{ km/h}} \approx 0.04878 \text{ hours}
\]
3. **Convert hours to minutes**:
- To convert hours to minutes, we multiply by 60:
\[
0.04878 \text{ hours} \times 60 \approx 2.9268 \text{ minutes}
\]
4. **Round to the nearest minute**:
- Rounding 2.9268 gives us approximately 3 minutes.
Thus, the time until they meet is approximately:
**0 hours and 3 minutes.**
1. **Calculate the combined speed**:
- The whale is swimming north at 40 km/h.
- The boat is traveling south at 83 km/h.
- Thus, the combined speed of the whale and the boat is:
\[
\text{Combined speed} = 40 \text{ km/h} + 83 \text{ km/h} = 123 \text{ km/h}
\]
2. **Calculate the time until they meet**:
- They are 6 kilometers apart, and they are closing this gap at a relative speed of 123 km/h. We can use the formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]
Using the values we have:
\[
\text{Time} = \frac{6 \text{ km}}{123 \text{ km/h}} \approx 0.04878 \text{ hours}
\]
3. **Convert hours to minutes**:
- To convert hours to minutes, we multiply by 60:
\[
0.04878 \text{ hours} \times 60 \approx 2.9268 \text{ minutes}
\]
4. **Round to the nearest minute**:
- Rounding 2.9268 gives us approximately 3 minutes.
Thus, the time until they meet is approximately:
**0 hours and 3 minutes.**