Boat Crossing River, Lake
Date: 8/3/96 at 23:12:49 From: Y. Samarasekera Subject: Boat Crossing River, Lake Dear Dr. Math, Please help! I have no idea how to do this problem. Points A and B are on the banks of a river. It takes a motorboat one hour to go downstream from A to B, and 1 hour 30 mins to go upstream from B to A. How long would it take the motorboat to go between points C and D on the shore of a lake if the distance between C and D is the same as that between A and B? Thank you. Tanya
Date: 8/4/96 at 8:26:44 From: Doctor Anthony Subject: Re: Boat Crossing River, Lake In this type of problem you must have letters to represent the various unknowns; then you can write down equations to represent the information given. Let x = distance A to B Let u = speed of current of the river Let v = speed of boat in still water. Now using the equation: time = distance/speed we have For downstream time x/(v+u) = 1 ........(1) For upstream time x/(v-u) = 1.5 .......(2) For time on the lake we must find x/v From (1) x = v+u From (2) x = 1.5v - 1.5u We must eliminate u from these two equations Multiply (1) by 1.5 1.5x = 1.5v + 1.5u and (2) gives x = 1.5v - 1.5u --------------------- adding 2.5x = 3v x/v = 3/2.5 = 1.2 hours = 1 hour 12 minutes. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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