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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 1, 2024

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First, let's start by calculating the distance Willl covers before Grace even can start. We have:

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

This means that when Grace starts to row, she and Will have \((2800 m) – (2250 m) = 550 m\)to cover before meeting up.

We have them rowing at each other at the same exact time, so we have \((50)(t) + (30)(t) = 550\) where t is the time it takes.

Now, we solve for t,

\(80t = 550 \\ t = 550/80 = 6.875\)

This is approximately 6 minutes and 52 seconds.

We add this on to the 45 minutes it took Will to row, and add that time onto 2 P.M.

We get that Will and Grace meet at \(2:51:52\) P.M.

Thanks! :)

Jun 1, 2024