Two groups of tourists are on the same floor of a skyscraper they are visiting, and they board adjacent elevators at the same time. The first group is headed up at a speed of $140$ meters per minute. The second is headed down at a speed of $290$ meters per minute. How long will it be before the elevators are $360$ meters apart? If necessary, round your answer to the nearest second. $\newline$ minutes and seconds

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Q. Two groups of tourists are on the same floor of a skyscraper they are visiting, and they board adjacent elevators at the same time. The first group is headed up at a speed of

140

meters per minute. The second is headed down at a speed of

290

meters per minute. How long will it be before the elevators are

360

meters apart? If necessary, round your answer to the nearest second.

\newline

____ minutes and ____ seconds

Calculate Combined Speed: Calculate the combined speed of the two elevators moving in opposite directions. $\newline$ Speed of first elevator: $140$ meters per minute $\newline$ Speed of second elevator: $290$ meters per minute $\newline$ Combined speed = Speed of first elevator + Speed of second elevator $\newline$ Combined speed = $140 + 290$ $\newline$ Combined speed = $430$ meters per minute
Determine Time Apart: Determine the time it takes for the elevators to be $360$ meters apart using the combined speed. $\newline$ Distance to be apart = $360$ meters $\newline$ Time = Distance / Combined speed $\newline$ Time = $360 / 430$ $\newline$ Time $\approx 0.8372$ minutes
Convert Time to Seconds: Convert the time from minutes to minutes and seconds. $\newline$ $0.8372$ minutes is the same as $0.8372 \times 60$ seconds. $\newline$ $0.8372 \times 60 \approx 50.232$ seconds $\newline$ Since we need to round to the nearest second, we get approximately $50$ seconds.
Final Time Calculation: Since the time in minutes is less than one minute, we only have seconds to consider. $\newline$ Therefore, the elevators will be $360$ meters apart in $0$ minutes and $50$ seconds.