Mrs. Richmond's class is on a ferry that is traveling $41$ kilometers per hour. The students notice that they are passing right by a fishing boat that is traveling in exactly the opposite direction at $89$ kilometers per hour. How long will it be before the two vessels are $6$ kilometers apart? $\newline$ If necessary, round your answer to the nearest minute. $\newline$ hours and minutes $\newline$

Full solution

Q. Mrs. Richmond's class is on a ferry that is traveling

41

kilometers per hour. The students notice that they are passing right by a fishing boat that is traveling in exactly the opposite direction at

89

kilometers per hour. How long will it be before the two vessels are

6

kilometers apart?

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If necessary, round your answer to the nearest minute.

\newline

____ hours and ____ minutes

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Calculate Speed: Calculate the combined speed of the ferry and the fishing boat. $\newline$ Speed of ferry: $41$ kilometers per hour $\newline$ Speed of fishing boat: $89$ kilometers per hour $\newline$ Since they are traveling in opposite directions, their speeds add up. $\newline$ Combined speed = Speed of ferry + Speed of fishing boat $\newline$ Combined speed = $41 + 89$ $\newline$ Combined speed = $130$ kilometers per hour
Calculate Time: Calculate the time it takes for the two vessels to be $6$ kilometers apart. $\newline$ Distance to be apart: $6$ kilometers $\newline$ Combined speed: $130$ kilometers per hour $\newline$ Time $=$ Distance $/$ Speed $\newline$ Time $=$ $6$ $/$ $130$ $\newline$ Time $hickapprox$ $6$ $0$ hours
Convert to Minutes: Convert the time from hours to minutes. $\newline$ Time in hours: $0.04615$ $\newline$ Minutes in an hour: $60$ $\newline$ Time in minutes = Time in hours $\times$ Minutes in an hour $\newline$ Time in minutes = $0.04615 \times 60$ $\newline$ Time in minutes $\approx 2.769$ , which we round to the nearest minute. $\newline$ Time in minutes $\approx 3$ minutes
Express Time in Hours: Express the time before the two vessels are $6$ kilometers apart in hours and minutes. $\newline$ Since the time in hours was less than one hour, it is $0$ hours. $\newline$ The time in minutes is $3$ minutes. $\newline$ So, it will be $0$ hours and $3$ minutes before the two vessels are $6$ kilometers apart.