Hakim and Frank just finished a picnic at the park and are about to ride their bikes home. Hakim goes $14$ miles per hour, and Frank goes $11$ miles per hour in precisely the opposite direction. In how long will they be $6$ miles apart? If necessary, round your answer to the nearest minute. $\newline$ hours and minutes $\newline$

Full solution

Q. Hakim and Frank just finished a picnic at the park and are about to ride their bikes home. Hakim goes

14

miles per hour, and Frank goes

11

miles per hour in precisely the opposite direction. In how long will they be

6

miles apart? If necessary, round your answer to the nearest minute.

\newline

____ hours and ____ minutes

\newline

Calculate Relative Speed: We need to find the time it takes for Hakim and Frank to be $6$ miles apart. Since they are traveling in opposite directions, we can add their speeds together to find the relative speed at which they are moving apart. $\newline$ Speed of Hakim: $14$ miles per hour $\newline$ Speed of Frank: $11$ miles per hour $\newline$ Relative speed = Speed of Hakim + Speed of Frank $\newline$ Relative speed = $14 + 11 = 25$ miles per hour
Calculate Time: Now that we have the relative speed, we can calculate the time it takes for them to be $6$ miles apart using the formula: $\newline$ Time $=$ Distance $/$ Speed $\newline$ We have a distance of $6$ miles and a relative speed of $25$ miles per hour. $\newline$ Time $=$ $6 / 25$ $\newline$ Time $=$ $0.24$ hours
Convert to Minutes: To convert the time from hours to minutes, we multiply by $60$ since there are $60$ minutes in an hour. $\newline$ Time in minutes = $0.24$ hours $\times 60$ minutes/hour $\newline$ Time in minutes = $14.4$ minutes $\newline$ Since we need to round to the nearest minute, we round $14.4$ minutes to $14$ minutes.
Final Time Calculation: We can see that $0.24$ hours is less than one hour, so the number of hours is $0$ . The number of minutes is $14$ . Therefore, Hakim and Frank will be $6$ miles apart in $0$ hours and $14$ minutes.