Question

Use the descriptions to identify the variables that need to be solved for and the equations

needed to solve.
3) Traveling downstream a certain boat went 9 km/h. Traveling upstream it only went 1 km/h. Find
the speed of the boat in still water and the speed of the current. what’s the equation

Answer 1

The speed of the boat in still water is 5 km/h, and the speed of the current is 4 km/h, obtained by solving two equations that are set up based on the given upstream and downstream speeds.

Step-by-step explanation:

To find the speed of the boat in still water and the speed of the current, we can let 'b' represent the boat's speed in still water and 'c' represent the current's speed. We have two scenarios: downstream and upstream. Going downstream, the boat's speed is aided by the current, so the total speed is b + c. Upstream, the boat's speed is hindered by the current, so the total speed is b - c. According to the question, the boat's downstream speed is 9 km/h, and upstream speed is 1 km/h.

We can now write down two equations based on these scenarios:

1. b + c = 9 (downstream equation)
2. b - c = 1 (upstream equation)

To solve for 'b' and 'c', we can use these two equations together. Here's a step-by-step method:

1. Add the two equations to eliminate 'c': (b + c) + (b - c) = 9 + 1, which simplifies to 2b = 10.
2. Divide both sides by 2 to find the boat's speed in still water: b = 5 km/h.
3. Subtract the second equation from the first one to find the speed of the current: (b + c) - (b - c) = 9 - 1, which simplifies to 2c = 8, and c = 4 km/h after division by 2.

Therefore, the speed of the boat in still water is 5 km/h, and the speed of the current is 4 km/h.