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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?

Jul 21, 2024

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First, let's calculate the distance Will travels before grace even leaves.

Since he traveled for 45 minutes, we have

\((45 min)(50 m/min) = 2250 m \)

So when Grace starts, she and Will have

\((2800 m) – (2250 m) = 550 m \) 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

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

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 \(2:52:52\)

Thanks! :)

Jul 21, 2024
edited by NotThatSmart  Jul 21, 2024