How Wide is the River?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? 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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