Lily can row 5 miles per hour in still water. It takes her as long to row 4 miles upstream as 16 miles downstream. How fast in the current?
r=d/t
r=d/t
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let x = time
let y = speed of the current
x(5 - y) = 4
x = 4 / (5 - y)
x(5 + y) = 16
x = 16 / (5 + y)
4 / (5 - y) = 16 / (5 + y)
4(5 + y) = 16(5 - y)
20 + 4y = 80 - 16y
20y = 60
y = 3
current is 3 mph
time is 2 hours
let y = speed of the current
x(5 - y) = 4
x = 4 / (5 - y)
x(5 + y) = 16
x = 16 / (5 + y)
4 / (5 - y) = 16 / (5 + y)
4(5 + y) = 16(5 - y)
20 + 4y = 80 - 16y
20y = 60
y = 3
current is 3 mph
time is 2 hours
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Just looking at it, the current is 3 MPH, but let's prove it analytically
Time = Distance/Speed and Time Upstream = Time Downstream, so
4/(5 - C) = 16/(5 + C)
1/( 5 - C) = 4/(5 + C)
5 + C = 20 - 4C
5C = 15
C = 3
Time = Distance/Speed and Time Upstream = Time Downstream, so
4/(5 - C) = 16/(5 + C)
1/( 5 - C) = 4/(5 + C)
5 + C = 20 - 4C
5C = 15
C = 3
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4 miles per hour because 16/4 is 4 miles per hour. If i got this wrong please dont be mad because I am only in 6th grade!