A rescue boat just picked up some sailors in a lifeboat. Now the rescue boat is heading north at $14$ miles per hour. The lifeboat, which they abandoned, is drifting south at a speed of $3$ miles per hour. How long will it be before the rescued sailors are $57$ miles from their lifeboat? $\newline$ If necessary, round your answer to the nearest minute. $\newline$ hours and minutes $\newline$

Full solution

Q. A rescue boat just picked up some sailors in a lifeboat. Now the rescue boat is heading north at

14

miles per hour. The lifeboat, which they abandoned, is drifting south at a speed of

3

miles per hour. How long will it be before the rescued sailors are

57

miles from their lifeboat?

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If necessary, round your answer to the nearest minute.

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____ hours and ____ minutes

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Calculate Combined Speed: Calculate the combined speed of the rescue boat and the lifeboat. $\newline$ The rescue boat is heading north at $14$ miles per hour, and the lifeboat is drifting south at $3$ miles per hour. Since they are moving in opposite directions, their speeds add up. $\newline$ Combined speed $=$ Speed of rescue boat $+$ Speed of lifeboat $\newline$ Combined speed $= 14 \, \text{mph} + 3 \, \text{mph}$ $\newline$ Combined speed $= 17 \, \text{mph}$
Calculate Time to Reach $57$ Miles: Calculate the time it will take for the sailors to be $57$ miles from their lifeboat. $\newline$ We need to find the time it takes for the two boats to be $57$ miles apart. $\newline$ Time $=$ Distance $/$ Speed $\newline$ Time $=$ $57$ miles $/$ $17$ mph $\newline$ Time $hickapprox$ $3.353$ hours
Convert Time to Hours and Minutes: Convert the time from hours to hours and minutes. $\newline$ Since we have a decimal hour, we need to convert it to minutes. There are $60$ minutes in an hour. $\newline$ Minutes $= (\text{Decimal part of the hour}) \times 60$ $\newline$ Minutes $\approx 0.353 \times 60$ $\newline$ Minutes $\approx 21.18$ minutes $\newline$ We round this to the nearest minute. $\newline$ Minutes $\approx 21$ minutes
Final Answer: Combine the whole number of hours with the rounded minutes to get the final answer. $\newline$ The sailors will be $57$ miles from their lifeboat in approximately $3$ hours and $21$ minutes.