A Coast Guard rescue craft just picked up the captain of a disabled sailboat. The rescue craft is now heading back to shore at a rate of $48$ miles per hour. Meanwhile, the sailboat is drifting in the other direction at $3$ miles per hour. How long will it be before the rescue craft is $41$ miles from the sailboat? $\newline$ If necessary, round your answer to the nearest minute. $\newline$ hours and minutes $\newline$

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Q. A Coast Guard rescue craft just picked up the captain of a disabled sailboat. The rescue craft is now heading back to shore at a rate of

48

miles per hour. Meanwhile, the sailboat is drifting in the other direction at

3

miles per hour. How long will it be before the rescue craft is

41

miles from the sailboat?

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If necessary, round your answer to the nearest minute.

\newline

____ hours and ____ minutes

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Calculate Combined Speed: Determine the combined rate at which the distance between the rescue craft and the sailboat is increasing. $\newline$ Since the rescue craft is moving away from the sailboat, we add their speeds to find the rate at which the distance between them increases. $\newline$ Speed of rescue craft: $48$ miles per hour $\newline$ Speed of sailboat: $3$ miles per hour $\newline$ Combined speed = Speed of rescue craft + Speed of sailboat $\newline$ Combined speed = $48 + 3 = 51$ miles per hour
Find Time to Cover Distance: Calculate the time it will take for the rescue craft to be $41$ miles away from the sailboat. $\newline$ We use the formula $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$ to find the time it will take for the rescue craft to be $41$ miles away from the sailboat. $\newline$ Distance to be covered: $41$ miles $\newline$ Combined speed: $51$ miles per hour $\newline$ $\text{Time} = \frac{\text{Distance}}{\text{Combined speed}}$ $\newline$ $\text{Time} = \frac{41}{51}$ $\newline$ $\text{Time} \approx 0.8039$ hours
Convert Time to Minutes: Convert the time from hours to minutes and round to the nearest minute if necessary. $\newline$ To convert hours to minutes, we multiply by $60$ . $\newline$ Time in minutes $=$ Time in hours $\times 60$ $\newline$ Time in minutes $\approx 0.8039 \times 60$ $\newline$ Time in minutes $\approx 48.234$ minutes $\newline$ Since we need to round to the nearest minute, the time is approximately $48$ minutes.