It takes a boat going upstream 11 hours and 9 hours downstream. what is the speed of the boat if the current is 2mph

Remark
You don't need the distance. The only thing that matters is the times (and assuming the same rate is used no matter what the current is doing). The distance coming and going is the same.

d_coming = d_going
t upstream = 11 hours
t downstream = 9 hours
current = 2 mph
rate_up = rate_down = r

General formula
d = r * t

Specific Formula
11(r - 2) = 9(r + 2) Note he seems faster with less time. That olnly means that the current is going in the same direction he is.

Solve
11(r - 2) = 9(r + 2)
11r - 11 =9r + 18    add 11 on both sides.
11r = 9r + 18 + 11  
11r = 9r + 29          subtract 9r from both sides.
11r - 9r = 29 
2r = 29                   divide by 2
r = 29/2
r = 14.5

Answer
The speed of the boat is 14.5 miles per hour.

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