Darnell and Roxanne just finished a picnic at the park and are about to ride their bikes home. Darnell goes $6$ miles per hour, and Roxanne goes $7$ miles per hour in precisely the opposite direction. In how long will they be $10$ miles apart? $\newline$ If necessary, round your answer to the nearest minute. $\newline$ hours and minutes $\newline$

Full solution

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

6

miles per hour, and Roxanne goes

7

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

10

miles apart?

\newline

If necessary, round your answer to the nearest minute.

\newline

____ hours and ____ minutes

\newline

Calculate Combined Speed: We have: $\newline$ Speed of Darnell: $6$ miles per hour $\newline$ Speed of Roxanne: $7$ miles per hour $\newline$ Since they are traveling in opposite directions, we need to find their combined speed. $\newline$ Combined speed = Speed of Darnell + Speed of Roxanne $\newline$ Combined speed = $6 + 7 = 13$ miles per hour
Find Time Taken: Now, we need to calculate the time it takes for them to be $10$ miles apart using their combined speed. $\newline$ Time $=$ Distance $/$ Speed $\newline$ Time $=$ $10$ miles $/$ $13$ miles per hour $\newline$ Time $hickapprox 0.769$ hours
Convert to Minutes: To convert hours into minutes, we multiply by $60$ . $\newline$ Time in minutes = $0.769$ hours $\times 60$ minutes/hour $\newline$ Time in minutes $\approx 46.15$ minutes $\newline$ Since we need to round to the nearest minute, we round $46.15$ to $46$ minutes.
Final Result: Therefore, Darnell and Roxanne will be $10$ miles apart in approximately $0$ hours and $46$ minutes.