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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 26, 2024
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avatar+1252 
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First, let's find the distance Will travels before Grace even starts rowing. 

Since Will has a 45 minute head start, we have the equation

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

 

This means that Will and Grace must cover

\((2800 m) – (2250 m) = 550 m \) together. 

 

Let's say the two row t minutes. Since we add their speeds together, we have

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

 

This rounds to about 6 minutes and 52 seconds. 

In total, the two took 51 minutes and 32 seconds to meet each other . So, the two will meet at \(2:51:52 pm \)

 

So 2:51:52 is our answer. 

 

Thanks! :)

 Jun 26, 2024

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