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Helen and Elizabeth just met up in Springdale for the afternoon, and now it is time for them to get in their cars and head home. Helen heads due east at $95$ kilometers per hour, and Elizabeth heads due west at $89$ kilometers per hour. How long will it be until they are $77$ kilometers apart? $\newline$ 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. Helen and Elizabeth just met up in Springdale for the afternoon, and now it is time for them to get in their cars and head home. Helen heads due east at

95

kilometers per hour, and Elizabeth heads due west at

89

kilometers per hour. How long will it be until they are

77

kilometers apart?

\newline

If necessary, round your answer to the nearest minute.

\newline

\_\_\_

hours and

\_\_\_

minutes

\newline

Find Combined Speed: We need to find the combined speed at which Helen and Elizabeth are moving apart. Since they are traveling in opposite directions, we add their speeds together. $\newline$ Speed of Helen: $95$ kilometers per hour $\newline$ Speed of Elizabeth: $89$ kilometers per hour $\newline$ Combined speed = Speed of Helen + Speed of Elizabeth $\newline$ Combined speed = $95 + 89$ $\newline$ Combined speed = $184$ kilometers per hour
Calculate Time: Now, we need to calculate the time it takes for them to be $77$ kilometers apart using their combined speed. $\newline$ Time $= \frac{\text{Distance}}{\text{Speed}}$ $\newline$ Time $= \frac{77 \text{ kilometers}}{184 \text{ kilometers per hour}}$ $\newline$ Time $\approx 0.4185$ hours
Convert to Minutes: To convert the time from hours to minutes, we multiply the decimal part by $60$ . $\newline$ $0.4185$ hours $\approx 0.4185 \times 60$ minutes $\newline$ $0.4185$ hours $\approx 25.11$ minutes $\newline$ Since we need to round to the nearest minute, we round $25.11$ minutes to $25$ minutes.
Final Time Calculation: Now we have the time in hours and minutes. $\newline$ Hours = $0$ (since $0.4185$ is less than $1$ hour) $\newline$ Minutes = $25$ $\newline$ So, Helen and Elizabeth will be $77$ kilometers apart in $0$ hours and $25$ minutes.

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