Question

Solve the following application problem. Be sure to show your system of equations and the steps to solve the problem.

Application Problem: 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 solve this application problem, we can create a system of equations using the given information and solve it to find the speed of the boat in still water and the speed of the current.

Step-by-step explanation:

To solve this application problem, we can create a system of equations using the information given. Let's assume that the speed of the boat in still water is represented by 'b' and the speed of the current is represented by 'c'.

When the boat is going downstream, the effective speed is 'b+c', and the time it takes to cover 16 miles is 2 hours. Therefore, the equation becomes: 16/(b+c) = 2.

When the boat is going upstream, the effective speed is 'b-c', and the time it takes to cover 16 miles is 4 hours. Therefore, the equation becomes: 16/(b-c) = 4.

Now, we can solve this system of equations to find the speed of the boat in still water and the speed of the current.

Answer 2

• boat: 6 mph
• current: 2 mph

Step-by-step explanation:

The relationship between time, speed, and distance is ...

speed = distance/time

For boat speed b and current speed c, the speed downstream is ...

b +c = (16 mi)/(2 h) = 8 mi/h

The speed upstream is ...

b -c = (16 mi)/(4 h) = 4 mi/h

Adding the two equations eliminates the c term:

2b = 12 mi/h

b = 6 mi/h . . . . . divide by 2

Solving the second equation for c, we get ...

c = b -4 mi/h = 6 mi/h -4 mi/h = 2 mi/h

The speed of the boat in still water is 6 mi/h; the current is 2 mi/h.