Question

It takes three hours for a boat to go 18 miles downstream, and nine hours to return. What is the rate of the boat in calm water and the rate of the current?​

Answer 1

The boat's rate in calm water is 4 miles/hour, and the rate of the current is 2 miles/hour. This is found by setting up a system of equations using the times and distances given for downstream and upstream travel and solving for the boat's speed and the current's speed.

Step-by-step explanation:

The question involves determining the rate of the boat in calm water and the rate of the current given the time it takes for the boat to travel downstream and upstream a certain distance. To solve this problem, we can set up two equations using the formula distance = rate × time. Let's define b as the boat's speed in calm water and c as the current's speed.

• Downstream: the boat and current work together, so the speed is b + c. The equation for downstream is 18 miles = (b + c) × 3 hours.
• Upstream: the current works against the boat, so the speed is b - c. The equation for upstream is 18 miles = (b - c) × 9 hours.

To find the values of b and c, we solve the system of equations:

• 18 = 3(b + c)
• 18 = 9(b - c)

From the first equation, b + c = 6. From the second equation, b - c = 2. Adding these two equations, we get 2b = 8, so b = 4 miles/hour. Subtracting the second equation from the first, we get 2c = 4, so c = 2 miles/hour. Therefore, the boat's rate in calm water is 4 miles/hour and the current's rate is 2 miles/hour.

Answer 2

Step-by-step explanation:

Distance = rate × time

If B is the rate of the boat, and C is the rate of the current, then we can write two equations:

18 = (B + C) × 3

18 = (B − C) × 9

Simplifying the equations:

6 = B + C

2 = B − C

Add the equations together to eliminate C:

8 = 2B

B = 4

Plug into either equation to find C:

C = 2

The boat's rate is 4 mph, and the current's rate is 2 mph.