+1734 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?
+34 Will rows for 45 minutes until Grace starts. In that time Will advances 45⋅50=2250 meters. Every minute they get 80 meters closer to each other. At the time Grace starts, they will be 550 meters apart. It will take 55080minutes, which is around 7 minutes. They will meet at around 2:52.
+1946 First, let's calculate the distance Will travels before grace even leaves.
Since he traveled for 45 minutes, we have
(45min)(50m/min)=2250m
So when Grace starts, she and Will have
(2800m)–(2250m)=550m to cover.
Let's let t be the amount of time it takes for the two to catch up to each other after Grace starts rowing.
We have the equation
(50)(t)+(30)(t)=55080t=550t=550/80=6.875
This is approximately 6 minutes and 52 seconds.
So the clock time they meet is 6 min 52 sec after Grace starts.
Grace started at 2:45, so add 6 min 52 sec and the clock will read 2:51:52 pm when they meet
Thus, our final answer is 2:51:52
Thanks! :)
