Zane and Camilla are coworkers who live in different cities. They both left the office at the same time today. Camilla drove directly east toward Oxford at a speed of $37$ miles per hour. Zane took the bus directly west toward Westminster, traveling $32$ miles per hour. In how long were the two of them $44$ miles apart? $\newline$ If necessary, round your answer to the nearest minute. $\newline$ hours and minutes $\newline$

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Q. Zane and Camilla are coworkers who live in different cities. They both left the office at the same time today. Camilla drove directly east toward Oxford at a speed of

37

miles per hour. Zane took the bus directly west toward Westminster, traveling

32

miles per hour. In how long were the two of them

44

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 Camilla: $37$ miles per hour (eastward) $\newline$ Speed of Zane: $32$ miles per hour (westward) $\newline$ Since they are traveling in opposite directions, we need to find their combined speed. $\newline$ Combined speed = Speed of Camilla + Speed of Zane $\newline$ Combined speed = $37$ mph + $32$ mph $\newline$ Combined speed = $69$ mph
Find Time: Now, we need to calculate the time it takes for them to be $44$ miles apart. $\newline$ Time $= \frac{\text{Distance}}{\text{Speed}}$ $\newline$ We will use the combined speed and the distance they need to be apart. $\newline$ Time $= \frac{44 \text{ miles}}{69 \text{ miles per hour}}$
Perform Division: Perform the division to find the time in hours. $\newline$ Time $\approx \frac{44}{69}$ $\newline$ Time $\approx 0.6377$ hours
Convert to Minutes: To convert the time from hours to minutes, we multiply by $60$ (since there are $60$ minutes in an hour). $\newline$ Minutes = $0.6377$ hours $\times 60$ minutes/hour $\newline$ Minutes $\approx 38.262$ minutes
Round to Nearest: We round the minutes to the nearest whole number. $\newline$ Minutes $\approx 38$ minutes $\newline$ Since the time in hours was less than one, we have $0$ hours and $38$ minutes.