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?

Question

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

Answer 1

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.