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

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

3 Online Users