Barbara is kayaking on a river in Clinton County, moving down the river at a speed of $8$ miles per hour. Meanwhile, Levi is on a jet ski $5$ miles away, moving up the river at $27$ miles per hour. How long will it be before the two meet? $\newline$ If necessary, round your answer to the nearest minute. $\newline$ hours and minutes $\newline$

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Rate of travel: word problems

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Q. Barbara is kayaking on a river in Clinton County, moving down the river at a speed of

8

miles per hour. Meanwhile, Levi is on a jet ski

5

miles away, moving up the river at

27

miles per hour. How long will it be before the two meet?

\newline

If necessary, round your answer to the nearest minute.

\newline

____ hours and ____ minutes

\newline

Calculate Combined Speed: Calculate the combined speed of Barbara and Levi. $\newline$ Barbara's speed: $8$ miles per hour (down the river) $\newline$ Levi's speed: $27$ miles per hour (up the river) $\newline$ Since they are moving towards each other, we add their speeds to find the combined speed. $\newline$ Combined speed = Barbara's speed + Levi's speed $\newline$ Combined speed = $8$ mph + $27$ mph $\newline$ Combined speed = $35$ mph
Calculate Meeting Time: Calculate the time it will take for Barbara and Levi to meet. $\newline$ They are $5$ miles apart, and we need to find the time it takes to cover this distance at their combined speed. $\newline$ Time $=$ Distance $/$ Speed $\newline$ Time $=$ $5$ miles $/$ $35$ miles per hour $\newline$ Time $hickapprox 0.1429$ hours
Convert to Minutes: Convert the time from hours to minutes. $\newline$ Since there are $60$ minutes in an hour, we multiply the time in hours by $60$ to find the time in minutes. $\newline$ Time in minutes $=$ Time in hours $\times 60$ minutes per hour $\newline$ Time in minutes $\approx 0.1429$ hours $\times 60$ minutes per hour $\newline$ Time in minutes $\approx 8.57$ minutes
Round to Nearest Minute: Round the time to the nearest minute. $\newline$ Time in minutes $\approx 8.57$ minutes $\newline$ Rounded time = $9$ minutes (since $0.57$ is closer to $1$ than to $0$ )
Express in Hours and Minutes: Express the time in hours and minutes. $\newline$ Since the time is less than one hour, the number of hours is $0$ . $\newline$ Final time = $0$ hours and $9$ minutes