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Will and Grace are canoeing on a lake.  Will rows at $50$ meters per minute and Grace rows at $30$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}45$ p.m. If they always row directly towards each other, and the lake is $2800$ meters across from the west side of the lake to the east side, at what time will the two meet?

 Jun 1, 2024
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First, let's start by calculating the distance Willl covers before Grace even can start. We have:

\((45 min)(50 m/min) = 2250 m\)

 

This means that when Grace starts to row, she and Will have \((2800 m) – (2250 m) = 550 m\)to cover before meeting up.

 

We have them rowing at each other at the same exact time, so we have \((50)(t) + (30)(t) = 550\) where t is the time it takes. 

 

Now, we solve for t, 

\(80t = 550 \\ t = 550/80 = 6.875\)

 

This is approximately 6 minutes and 52 seconds. 

 

We add this on to the 45 minutes it took Will to row, and add that time onto 2 P.M. 

 

We get that Will and Grace meet at \(2:51:52\) P.M.

 

Thanks! :) 

 Jun 1, 2024

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