SOLUTION: There are two boats that start out on opposite sides of a river at the same time. Each one is heading across the river to the other side. They each go a constant speed throughout

Question 791488: There are two boats that start out on opposite sides of a river at the same time. Each one is heading across the river to the other side. They each go a constant speed throughout the entire problem (so ignore having to slow down to turn around, and ignore current, etc.), but they are not necessarily the same speed as each other. When each boat reaches its opposite bank, it immediately turns around and heads back to where it started. The boats thus pass each other twice.
The first time they pass, they are 700 yards from one of the banks of the river.
The second time they pass; they have each turned around after reaching their respective opposite shores and have stated back toward where they each began. When they pass the second time, they are 300 yard from the other bank of the river. How wide is the river?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
here are two boats that start out on opposite sides of a river at the same time.
Each one is heading across the river to the other side.
They each go a constant speed throughout the entire problem (so ignore having to slow down to turn around, and ignore current, etc.), but they are not necessarily the same speed as each other.
When each boat reaches its opposite bank, it immediately turns around and heads back to where it started.
The boats thus pass each other twice.
The first time they pass, they are 700 yards from one of the banks of the river.
The second time they pass; they have each turned around after reaching their respective opposite shores and have stated back toward where they each began.
When they pass the second time, they are 300 yard from the other bank of the river.
How wide is the river?
:
Let x = the width of the river
The first meeting
Boat 1 travels 700 yds
Boat 2 travels (x-700) yds
:
The 2nd meeting
Boat 1 travels (x-700) + 300 = (x-400) yds
Boat 2 travels 700 + (x-300) = (x+400) yds
:
the relationship of the distances each traveled, is the same to both meetings
=
cross multiply
700(x+400) = (x-700)(x-400)
FOIL
700x + 280000 = x^2 - 400x - 700x + 28000
700x + 280000 = x^2 - 1100x + 280000
Combine like terms on the right
0 = x^2 - 1100x - 700x + 280000 - 280000
x^2 - 1800x = 0
Factor
x(x - 1800) = 0
x = 1800 yds across the river

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