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).
(In reply to
Can someone please tell me where I went wrong ? by Dan)
Sure Dan,
You were mistaken about what happens in time interval t2.
You wrote:
"In time interval t2, A sails X-700 yards west, then X-300 yards east, for a total of 2X-1000 yards, while B sails 700 yards east and 300 yards west, for a total of 1000.
You should have written:
In time interval t2, A sails X-700 yards West, then 300 yards East, for a total of X-400 yards, while B sails 700 yards East and X-300 yards West, for a total of X+400 yards
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Then when you set up your equations you would have done:
700/(X-700) = (X-400)/(X+400)
... cross multiply ...
700X + 280000 = X² - 1100X + 280000
700X = X² - 1100X
0 = X² - 1800X
0 = X(X-1800)
X = 1800 (throwing away the zero)
(and this is somewhat similar to what Charlie did)
re: Can someone please tell me where I went wrong ?
