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Unread 10-04-2005, 21:09
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Re: How wide is the river?

Two ferry boats start at the same instant on opposite sides of the river. One is faster than the other. They cross at a point 720 yards from the left shore on their way to their respective destinations, where each one spends 10 minutes to change passengers before the return trip. They meet again at a point 400 yards from the right shore.
How wide is the river?

I tried to draw a picture but it wouldn't load...essentially what happens is...and this might be totally wrong since I am not feeilng up to reading that whole solution thing.

Boat #1 is the one on the left side of the river, and boat #2 is on the right side, so at the beginning, boat #1 travels 720 feet until it meets boat #2. Boat #2 goes "E" yards from the right side, before it first meets Boat #1. It then travels 720 feet further across the river. The length of the river is for now, r = 720 + e.

Distance = velocity * time

So, for now, in regards to their first meeting, 720 = v1 * T(a), and e = v2 * T(a). That time is the same becuase they took the same amount of time to go those respective distances. So then, Boat #2 travels 720 more yards at v2 in some more time, and thus 720 + e = v2 * (t(a) + t(b)). Looking at Boat #1, it goes that E distance at v1, at what we'll call time c. OK, so then, 720 + e = v1 * (t(a) + t(c)). Using the transitive property, we find that...

(v2)(TA) + (v2)(Tb) = (V1)(ta) + (V1)(Tc)
or
(V2)(TA + TB) = (V1)(TA + TC)

That's how far I am right now, I am deciding how to add the next factor...I hope it kinda helps...
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