Question

A tugboat travels 27 miles upstream and 13 miles downstream in 3 hours. If the boat travels 15 mph in calm water, how fast is the current?

a) 5.8 mph
b) 7.9 mph
c) 3.2 mph
d) 3.4 mph
e) 3.6 mph

Answer 1

The speed of the current is 3.4 mph.

Step-by-step explanation:

To calculate the speed of the current, we need to set up a system of equations based on the given information. Let's assume the speed of the current is x mph.

When the tugboat is traveling upstream, against the current, its effective speed is 15 - x mph. The distance traveled upstream is 27 miles.

When the tugboat is traveling downstream, with the current, its effective speed is 15 + x mph. The distance traveled downstream is 13 miles.

We can set up the equation 27/(15 - x) + 13/(15 + x) = 3, based on the fact that the total time taken for the upstream and downstream journeys is 3 hours.

Solving this equation, we find that x = 3.4 mph. So, the speed of the current is 3.4 mph.