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).

i drew out the scenario on graph paper, tried a few numerical guesses and stumbled upon a scenario that fits the problem:

the river is 1800 yards. picture a number line from shore A (0) to shore B (1800).

boat A travels 1100 yards from shore A and meets boat B which has travelled 700 yards from shore B.
when boat A travels another 1100 yards, it has arrived at shore B and turned and travelled to yard 1400, while boat B has travelled 700 yards to yard 400.
when boat A travels another 1100 yards, it has arrived at yard 300, meeting boat B which has gone the remaining yards to shore A, turned and gone 300 yards.

wording the answer to this problem has taken me more time than solving it, but i guess that's part of it. elegance is the goal in mathematics and my answer has had very little of it.

it was a fun problem anyway.

Posted by rixar on 2004-07-23 21:03:33