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 16, 2024

First, let's find how far Will gets before Grace even starts to row. 

We have the handy equation \(d=rt\) where d is distance, r is rate, and t is time. 

We have \( (45 min)(50 m/min) = 2250 m \), so will paddled 2250m before Grace started. 


When Grace starts to canoe, the two have \((2800 m) – (2250 m) = 550 m \) before they meet up. 

Thus, we can write the equation


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


This rounds to approximately 6 minutes and 52 seconds. 

This means the two spent about \(51:52\) minutes to meet eachother. 


This means they met each other at \(2:51:52 pm\)


So 2:51:52 is our final answer. 


Thanks! :)

 Jun 17, 2024

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