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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 9, 2024
 #1
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First, let's calculate how far Will got before Grace even started to row, 

 

We have \(d=st\), where d is distance, s is speed, and t is time. 

 

We have \((45 min)(50 m/min) = 2250 m \). Will rowed 2250m before Grace began. 

 

Now, Will and Grace have to cover \((2800 m) – (2250 m) = 550 m \) together. 

 

We have 

\( (50)(t) + (30)(t) = 550 \\ 80t = 550 \\ t = 550/80 = 6.875 \)

 

6.875 minutes is about 6 minutes and 52 seconds. 

 

The two started at 6:45, so they arrive at about \(6:51:52\) P.M. when they meet. 

 

Thanks! :)

 Jun 10, 2024

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