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

Well the speed of the boat changes depending on if it is up or down stream.

if it is going down stream it is with the current so there is a 2 mph assistance.

if upstream then 2 mph resistance.

i feel like there should be a given distance

11 hours to get to where, how far?

or simply answer 11-2=9 and 9+2=11. So possibly average it at 10.

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.