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).
1800 yards
Set up the problem:
t = the amount of time to first meeting
u = the amount of time to second meeting
w = width of river
x is rate of the boat 1
y is rate of the boat 2
(at their first meeting, they have traversed the width together, once)
xt + yt = w
xt = 700 (similarly
yt = w -700
(at their second meeting, they have traversed the width
together, three times)
xu + yu = 3w
and the other boat (speed y) has come to within 300 yards of the other side so:
yu = 2w - 300
And since they've traversed the river 3 times at constant speeds, this takes 3 times the original time so
u=3t.
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Combine equations
xu + 2w - 300 = 3w
xu - 300 = w
3xt - 300 = w
2100 - 300 = w
w = 1800 yards
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