Question 157391: A cruise boat travels 48 miles downstream in 3 hours and returns upstream in 6 hours. Find the rate of the stream.
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! let B = rate or boat.
let S = rate of stream.
rate * time = distance.
going downstream, the rate of travel is the rate of the boat plus the rate of the stream.
going upstream, the rate of travel is the rate of the boat minus the rate of the stream.
in equation form, this becomes.
(B+S)*3=48 (going downstream)
(B-S)*6=48 (going upstream)
since the distance is the same both times, these equations are equal to each other.
(B+S)*3=(B-S)*6
multiplying out.
becomes 3*B+3*S=6*B-6*S
becomes 9*S=3*B
becomes B=3*S
in the going downstream equation, 3*B+3*S = 48.
substituting 3*S for B, the equation becomes 3*(3*S) + 3*S = 48
which becomes 9*S + 3*S = 48
which becomes 12*S = 48
which becomes S = 4.
if S = 4, then the going downstream equation of 3*B + 3*S = 48
becomes 3*B + 12 = 48
becomes 3*B = 36
becomes B = 12.
the rate of the stream is 4 miles per hour and the rate of the boat is 12 miles per hour.
going downstream, the combined rate is 16 miles per hour.
48 miles / 16 yields 3 hours so math is confirmed for the downstream equation.
going upstream, the combined rate is 8 miles per hour.
48 miles / 8 yields 6 hours so math is confirmed for the upstream equation.
answer is the stream is traveling at 4 miles per hour downstream.
becomes
|
|
|
