Question

A small motor on a fishing boat can move the boat at a rate of 11 mph in calm water. Traveling with the current, the boat can travel 39 mi in the same amount of time it takes to travel 27 mi against the current. Find the rate of the current.

Answer 1

the answer to the question is 10mph

Answer 2

Speed of the boat = 11mph

Let the speed of the current be x

Downstream

Speed = (11 + x)

Distance = 39 miles

Time = Distance ÷ Speed

Time = 39/(11 + x)

Upstream:

Speed = (11 - x)

Distance = 27 miles

Time = Distance ÷ Speed

Time = 27/(11 - x)

Solve x :

Given that the time spent going upstream or downstream is the same

39/(11 + x) = 27/(11 - x)

39(11 - x) = 27( 11 + x)

429 - 39x = 297 + 27x

66x = 132

x = 2 mph

Answer: The rate of the current is 2 mph