Mrs. Brady's class takes a ferry east across a lake at $24$ miles per hour. At the same time, a fishing boat leaves from the opposite side of the lake, traveling west at $52$ miles per hour. The two vessels started out $1$ mile apart and are now traveling directly toward each other. How long will it be before they pass by each other? $\newline$ If necessary, round your answer to the nearest minute. $\newline$ hours and minutes

Full solution

Q. Mrs. Brady's class takes a ferry east across a lake at

24

miles per hour. At the same time, a fishing boat leaves from the opposite side of the lake, traveling west at

52

miles per hour. The two vessels started out

1

mile apart and are now traveling directly toward each other. How long will it be before they pass by each other?

\newline

If necessary, round your answer to the nearest minute.

\newline

____ hours and ____ minutes

Calculate combined speed: Calculate the combined speed of the ferry and the fishing boat. $\newline$ Speed of ferry: $24$ miles per hour $\newline$ Speed of fishing boat: $52$ miles per hour $\newline$ Combined speed $=$ Speed of ferry $+$ Speed of fishing boat $\newline$ Combined speed $= 24 + 52$ $\newline$ Combined speed $= 76$ miles per hour
Determine time taken: Determine the time it takes for the ferry and the fishing boat to cover the distance between them. $\newline$ Distance apart: $1$ mile $\newline$ Combined speed: $76$ miles per hour $\newline$ Time $=$ Distance $/$ Combined speed $\newline$ Time $=$ $1$ mile $/$ $76$ miles per hour $\newline$ Time $\approx 0.01316$ hours
Convert time to minutes: Convert the time from hours to minutes. $\newline$ Time in hours: $0.01316$ $\newline$ Minutes in an hour: $60$ $\newline$ Time in minutes = Time in hours $\times$ Minutes in an hour $\newline$ Time in minutes = $0.01316 \times 60$ $\newline$ Time in minutes $\approx 0.7896$ minutes
Round time to nearest minute: Round the time to the nearest minute. $\newline$ Time in minutes $\approx 0.7896$ $\newline$ Rounded time = $1$ minute (since we round to the nearest minute)