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# Algebra

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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 16, 2024

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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