Question

A boat that can travel 18 mph in still water can travel 21 miles downstream in the same amount of time that it can travel 15 miles upstream. Find the speed (in mph) of the current in the river.

Answer 1

Answer:

The speed of the current is 3 mph.

Step-by-step explanation:

The speed of he boat in calm water is "18 mph", the speed of the stream is "x" mph. When the boat is going downstream its speed is "x + 18", while when it goes upstream it will be "18-x". The time it takes for the boat to travel 21 miles downstream is:

$time = \frac{21}{x + 18}$

While the time it takes the boat to travel 15 miles upstream:

$time = \frac{15}{18 - x}$

Since the times are the same, we can make:

$\frac{21}{x + 18} = \frac{15}{18 -x}\\378 - 21x = 15x + 270\\21x + 15x = 378 - 270\\36x = 108\\x = 3 \text{ mph}$

The speed of the current is 3 mph.

Answer 2

Answer: The current of the water is 1.714 mph.