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A whale is swimming due north at a speed of $30$ miles per hour. Just $5$ miles away, a whale-watching tour boat is traveling south, directly toward the whale, at a speed of $46$ miles per hour. How long will it be before they meet? If necessary, round your answer to the nearest minute. $\_\_$ hours and $\_\_$ minutes

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Rate of travel: word problems

Full solution

Q. A whale is swimming due north at a speed of

30

miles per hour. Just

5

miles away, a whale-watching tour boat is traveling south, directly toward the whale, at a speed of

46

miles per hour. How long will it be before they meet? If necessary, round your answer to the nearest minute.

\_\_

hours and

\_\_

minutes

Calculate Speed: Calculate the combined speed of the whale and the boat. $\newline$ Speed of whale = $30 \, \text{mph}$ , Speed of boat = $46 \, \text{mph}$ . $\newline$ Combined speed = Speed of whale + Speed of boat = $30 \, \text{mph} + 46 \, \text{mph} = 76 \, \text{mph}$ .
Determine Time: Determine the time it will take for the whale and the boat to meet. $\newline$ Distance between them = $5$ miles. $\newline$ Time = Distance / Combined Speed = $\frac{5 \text{ miles}}{76 \text{ mph}} \approx 0.0658$ hours.
Convert to Minutes: Convert the time from hours to minutes. $\newline$ Time in minutes = $0.0658$ hours $\times 60$ minutes/hour $\approx 3.948$ minutes. $\newline$ Rounded to nearest minute = $4$ minutes.

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