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Two Boats and A River (Posted on 2003-11-13) Difficulty: 4 of 5
Two boats on opposite sides of a river head towards each other at different speeds. When they pass each other the first time they are 700 yards from one shoreline. They continue to the opposite shoreline, turn around, and move towards each other again. When they pass the second time they are 300 yards from the other shoreline.

How wide is the river? (Assume both boats travel at a constant speed and ignore factors such as turn-around time and the current of the river).

  Submitted by Ravi Raja    
Rating: 2.5000 (4 votes)
Solution: (Hide)
Define the following variables:

w=width of river

s1=speed of first boat

s2=speed of second boat

t1=time until boats meet the first time

t2=time until boats meet the second time

I shall arbitrarily say that both boats are 700 yards from the shore of original of the first boat at time t1.

The following equations can be inferred from the information given:

(1) w=t1*(s1+s2)

(2) s1*t1=700

(3) w+300=s1*t2

(4) 2w-300=s2*t2

Adding equations (1) and (2) we get:

(5) 3w=t2*(s1+s2)

Substituting s1+s2=w/t1 from equation (1) we get:

3w=t2*r/t1

3w*t1=r*t2

(6) 3*t1=t2

Combining equations (3) and (6):

(7) w+300=3*s1*t1

Combining equations (2) and (7):

w+300=2100

w=1800

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionSolutionDej Mar2008-07-16 00:59:06
AnswerK Sengupta2008-03-20 09:44:57
trial and errorrixar2004-07-23 21:03:33
SolutionSenthil Kumar2003-11-14 13:39:23
re(2): Can someone please tell me where I went wrong ?Dan2003-11-13 21:42:19
re: Can someone please tell me where I went wrong ?SilverKnight2003-11-13 21:11:38
QuestionCan someone please tell me where I went wrong ?Dan2003-11-13 20:53:05
re: In Defense of Limited EquationsSilverKnight2003-11-13 20:12:08
Current EventsDan2003-11-13 20:07:08
In Defense of Limited EquationsGordon Steel2003-11-13 19:50:07
re: Solution Without Almost No EquationsSilverKnight2003-11-13 16:05:53
Solution Without Almost No EquationsGordon Steel2003-11-13 15:16:49
SolutionsolutionCharlie2003-11-13 14:53:18
SolutionFull SolutionSilverKnight2003-11-13 14:43:06
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