SOLUTION: Two boats travel on a river between two towns and have the same two constant speeds: a high speed downstream and a low speed upstream. Boat 1 leaves town A as boat 2 leaves town B.

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Question 862027: Two boats travel on a river between two towns and have the same two constant speeds: a high speed downstream and a low speed upstream. Boat 1 leaves town A as boat 2 leaves town B. They pass each other 7 miles from town A, stop 4 minutes at their destinations, and pass again 9 miles from town A. What is the distance between the towns?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Two boats travel on a river between two towns and have the same two constant speeds:
a high speed downstream and a low speed upstream.
Boat 1 leaves town A as boat 2 leaves town B.
They pass each other 7 miles from town A, stop 4 minutes at their destinations, and pass again 9 miles from town A.
What is the distance between the towns?
:
let d = distance between A & B
:
At first meeting
Boat 1 travels 7 mi
Boat 2 travels (d-7)
At 2nd meeting
Boat 1 travels: (d-7)+(d-9) = 2d-16
Boat 2 travels: 7 + 9 = 16 mi
let x = the upstream speed
let y = the downstream speed
:
Write a time equation, time = dist/speed
First meeting
7%2Fx = %28%28d-7%29%29%2Fy
7y = x(d-7)
2nd meeting
%28%28d-7%29%29%2Fx + %28%28d-9%29%29%2Fy = 7%2Fy + 9%2Fx
mult by xy
y(d-7) + x(d-9) = 7x + 9y
dy - 7y + dx - 9x = 7x + 9y
dy + dx = 7x + 9x + 9y + 7y
d(x+y) = 16x + 16y
d(x+y) = 16(x+y)
divide both sides by (x+y)
d = 16 mi distance from A to B