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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 26, 2024

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First, let's find the distance Will travels before Grace even starts rowing.

Since Will has a 45 minute head start, we have the equation

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

This means that Will and Grace must cover

\((2800 m) – (2250 m) = 550 m \) together.

Let's say the two row t minutes. Since we add their speeds together, we have

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

This rounds to about 6 minutes and 52 seconds.

In total, the two took 51 minutes and 32 seconds to meet each other . So, the two will meet at \(2:51:52 pm \)