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Valentina boards an elevator in the lobby that is headed up at $610$ feet per minute. Meanwhile, $1,500$ feet above, Owen boards an adjacent elevator headed down at $620$ feet per minute. How long will it be before Valentina and Owen pass each other? $\newline$ If necessary, round your answer to the nearest second. $\newline$ minutes and seconds $\newline$

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Rate of travel: word problems

Full solution

Q. Valentina boards an elevator in the lobby that is headed up at

610

feet per minute. Meanwhile,

1,500

feet above, Owen boards an adjacent elevator headed down at

620

feet per minute. How long will it be before Valentina and Owen pass each other?

\newline

If necessary, round your answer to the nearest second.

\newline

____ minutes and ____ seconds

\newline

Calculate Combined Speed: Determine the combined speed at which Valentina and Owen are approaching each other. $\newline$ Valentina's speed: $610$ feet per minute $\newline$ Owen's speed: $620$ feet per minute $\newline$ Combined speed = Valentina's speed + Owen's speed $\newline$ Combined speed = $610 + 620$ $\newline$ Combined speed = $1230$ feet per minute
Find Passing Time: Calculate the time it will take for Valentina and Owen to pass each other. $\newline$ Distance between Valentina and Owen: $1500$ feet $\newline$ Combined speed: $1230$ feet per minute $\newline$ Time $=$ Distance $/$ Speed $\newline$ Time $=$ $1500$ $/$ $1230$ $\newline$ Time $hickapprox$ $1.2195$ minutes
Convert to Minutes and Seconds: Convert the time from minutes to minutes and seconds. $\newline$ Since there are $60$ seconds in a minute, we need to find out how many seconds are in the decimal part of the time calculated. $\newline$ $0.2195$ minutes $\times 60$ seconds/minute $\approx 13.17$ seconds $\newline$ So, Valentina and Owen will pass each other in approximately $1$ minute and $13$ seconds.

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