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### How Wide is the River?

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Date: Tue, 2 Jul 1996 13:12:53 -0400 (EDT)
From: Anonymous
Subject: two ferryboats

Two ferryboats ply back and forth across a river with constant
but different speeds, turning at the riverbanks without loss of time.
They leave opposite shores at the same instant, meet for the first
time 900 meters from one shore, and meet for the second time 500
meters from the opposite shore.

What is the width of the river?
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Date: Tue, 2 Jul 1996 16:16:56 -0400 (EDT)
From: Dr. Anthony
Subject: Re: two ferryboats

Let w = width of river, u = speed of faster boat, v = speed of
slower boat.

In the first situation, the faster boat has gone w-900 metres and the
slower boat 900 metres in the same time. So we have:

u/v = (w-900)/900

In the second situation the total distance of the faster boat is
w + w -500 and the distance travelled by the slower boat will be
w + 500. So we have:

u/v = (2w-500)/(w+500)

Equating these two values of u/v we get:

(w-900)/900 = (2w-500)/(w+500)

(w-900)(w+500) = 900(2w-500)

w^2 - 400w - 450000 = 1800w - 450000

w^2 - 2200w = 0

w(w-2200) = 0 and since w not equal to 0, we must have w = 2200

So the width of the river is 2200 metres.

-Doctor Anthony, The Math Forum

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Associated Topics:
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