Problema 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 the entire problem (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 started back toward where they each began. When they pass the second time, they are 300 yards from the other bank of the river. How wide is the river?
Answer provided by our tutors
step1 the distances traveled by the boats are proportional to their speeds
___ since the speeds are constant, the ratio of the distances is constant
step2 let w="width of river" ___ river is >700 yd wide
let x and y be the boat distances
step3 at first meeting ___ x=700, y=w-700
at second meeting ___ x=w+300, y=2w-300
ratio of distances is constant, so 700/(w-700)=(w+300)/(2w-300) ___ 1400w-210000=w^2-400w-210000
1400w=w^2-400w ___ 1800w=w^2 ___ 1800=w
steop4 the x and y values at the first meeting reversed
___ this resulted in a width <700