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?

Question

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?

Bot GPT 3.5 · Answer

We may consider this to be a meeting of Will and Grace's "two boats" traveling towards each other at $50+30=80$ meters per minute. The time difference was $45$ minutes. The distance they had to cover was $2800$ meters. Therefore, the two boats had to travel a combined total of $2800$ meters in $45$ minutes. Since they were traveling at a combined rate of $80$ meters per minute, it took them $\frac{2800}{80}=\boxed{35}$ minutes to do so. Since they started rowing at different times, the meeting must have occurred at $2: 45+35=3: 20$ p.m.