Two friends are windsurfing at a popular beach. Shawna is paddling out on her board, going $3$ miles per hour. At the same time, $2$ miles directly in front of Shawna, Peter has caught a big wave and is riding it back in at a rate of $15$ miles per hour. In how much time will the two surfers pass each other? $\newline$ If necessary, round your answer to the nearest minute. $\newline$ hours and minutes $\newline$

Full solution

Q. Two friends are windsurfing at a popular beach. Shawna is paddling out on her board, going

3

miles per hour. At the same time,

2

miles directly in front of Shawna, Peter has caught a big wave and is riding it back in at a rate of

15

miles per hour. In how much time will the two surfers pass each other?

\newline

If necessary, round your answer to the nearest minute.

\newline

____ hours and ____ minutes

\newline

Calculate Relative Speed: Determine the relative speed at which Shawna and Peter are moving towards each other. $\newline$ Speed of Shawna: $3$ miles per hour $\newline$ Speed of Peter: $15$ miles per hour $\newline$ Since they are moving towards each other, we add their speeds to get the relative speed. $\newline$ Relative speed $=$ Speed of Shawna $+$ Speed of Peter $\newline$ Relative speed $= 3 \, \text{mph} + 15 \, \text{mph}$ $\newline$ Relative speed $= 18$ miles per hour
Calculate Passing Time: Calculate the time it will take for them to pass each other. $\newline$ Distance between Shawna and Peter: $2$ miles $\newline$ Relative speed: $18$ miles per hour $\newline$ Time $=$ Distance $/$ Relative speed $\newline$ Time $=$ $2$ miles $/$ $18$ miles per hour $\newline$ Time $hickapprox 0.111$ hours
Convert Time to Minutes: Convert the time from hours to minutes. $\newline$ Time in hours: $0.111$ hours $\newline$ To convert to minutes, multiply by $60$ (since there are $60$ minutes in an hour). $\newline$ Time in minutes = $0.111$ hours $\times 60$ minutes/hour $\newline$ Time in minutes $\approx 6.666$ minutes $\newline$ Since we need to round to the nearest minute, we round $6.666$ minutes to $7$ minutes.