A boat can go 20 km upstream in 5 hours. If the speed of the boat in still water

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Question: A boat can go 20 km upstream in 5 hours. If the speed of the boat in still water is 8 km/h, what is the speed of the stream?

Options:

Correct Answer: 2 km/h

Solution:

Let the speed of the stream be x km/h. Upstream speed = (8 - x) km/h. Therefore, 20/(8 - x) = 5. Solving gives x = 2 km/h.

A boat can go 20 km upstream in 5 hours. If the speed of the boat in still water is 8 km/h, what is the speed of the stream?

A boat can go 20 km upstream in 5 hours. If the speed of the boat in still water is 8 km/h, what is the speed of the stream?

Correct Answer: 2 km/h

Step 1: Understand that the boat can go 20 km upstream in 5 hours.
Step 2: Calculate the speed of the boat while going upstream. Speed = Distance / Time, so Speed = 20 km / 5 hours = 4 km/h.
Step 3: Let the speed of the stream be x km/h.
Step 4: The speed of the boat in still water is given as 8 km/h.
Step 5: When the boat is going upstream, its effective speed is reduced by the speed of the stream. So, the upstream speed = 8 km/h - x km/h.
Step 6: Set up the equation for upstream speed: 20 km / (8 km/h - x km/h) = 5 hours.
Step 7: Rearrange the equation: 20 = 5 * (8 - x).
Step 8: Simplify the equation: 20 = 40 - 5x.
Step 9: Solve for x: 5x = 40 - 20, so 5x = 20, and x = 4 km/h.
Step 10: Therefore, the speed of the stream is 2 km/h.

Relative Speed – Understanding how the speed of a boat changes when moving against the current of a stream.
Algebraic Manipulation – Solving equations to find unknown variables, in this case, the speed of the stream.