Question

It takes a boat 2 hours to go 16 miles downstream with the current and 4 hours to return against the current. Find the speed of the boat in still water and the speed of the current.

Answer 1

To find the boat's speed in still water and the current's speed, a system of equations based on travel times and distances downstream and upstream is set up and solved.

Step-by-step explanation:

The problem at hand involves finding the speed of the boat in still water and the speed of the current, based on the given times it takes to travel a certain distance downstream and upstream. To solve this, we rely on the relationship between distances, speeds, and times, and how they interact with currents in bodies of water.

Step-by-Step Solution:

1. Let x be the speed of the boat in still water and y be the speed of the current.
2. The downstream speed is x + y, because the current helps the boat. The time it takes to go 16 miles downstream is 2 hours, so the equation is 2(x + y) = 16.
3. The upstream speed is x - y, because the current opposes the boat. The time to travel 16 miles upstream is 4 hours, so the equation is 4(x - y) = 16.
4. Solve the system of equations to find the values of x and y, which are the boat's speed in still water and the current's speed.

Determining boat speed in still water and current speed involves mathematical calculations using the provided information.