A motorboat can maintain a constant speed of 11 miles per hour relative to the water. The boat makes a trip upstream in 41 minutes and the return trip takes 22 minutes. What is the speed of the current?
A) 0.3 mph
B) 11 mph
C) 3.3 mph
D) 22 mph

Question

Quizplus · Accepted Answer

The speed of the boat relative to the water is 11 mph. Let the speed of the current be $c$ mph. When going upstream, the effective speed of the boat is $11 - c$ mph, and when going downstream, it's $11 + c$ mph. The time taken for the upstream trip is 41 minutes ($\frac{41}{60}$ hours) and for the downstream trip is 22 minutes ($\frac{22}{60}$ hours). Let the distance of the trip in one direction be $d$ miles. We can set up the equations based on the formula $distance = speed \times time$:For upstream: $d = (11 - c) \times \frac{41}{60}$For downstream: $d = (11 + c) \times \frac{22}{60}$Since the distances are the same, we can set the expressions equal to each other and solve for $c$:$(11 - c) \times \frac{41}{60} = (11 + c) \times \frac{22}{60}$Solving this equation gives $c = 3.3$ mph.

A Motorboat Can Maintain a Constant Speed of 11 Miles