Question 330939: Imagine a driver with straight parallel sides and no current. Boat a departs side A at the same time as boat b departs side B, both perpendicular to the riverbank, and both at constant (but possibly different) speeds. They pass each other 800 yards from A, proceed to the opposite shore, turn around, and pass again 400 yards from B. How wide is the river?
Answer by galactus(183)   (Show Source):
You can put this solution on YOUR website! Wow, this is a tricky little problem. But, doable I am sure.
No doubt, there are other ways to tackle this, but I am going to let
x=the speed of boat A and y=the speed of boat B.
Let w=the river width (I assume you mean a river and not a 'driver' :):)).
As with many problems, we can set up a ratio.
Since d=rt, we have t=d/r.
The distance they meet from bank A is 800 yds, then the distance from bank B is
w-800 yds. So, we have:
The next time they meet after they turn and head back, they are 400 yds from bank B. This time, boat B has turned from bank A and is heading back and meets boat A 400 yards from its shore, and boat A has turned at bank B and goes back 400 yards and meets boat B. Tricky to think about, huh?. We now have:
Now, we can hammer away at these until we have only w left.
Divide:
This simplifies down quite nicely. Equate:
Cross multiply:
Expand:
Assuming the river is not 0 yards wide, we have:
 yards.
That's over a mile wide. Big River.
I hope I didn't make a mistake after all that. WHEW! :):)
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