A boat travels 30 km downstream in 2 hours. If the speed of the stream is 5 km/h

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Question: A boat travels 30 km downstream in 2 hours. If the speed of the stream is 5 km/h, what is the speed of the boat in still water?

Options:

Correct Answer: 15 km/h

Solution:

Let the speed of the boat in still water be y km/h. Downstream speed = y + 5 km/h. Therefore, (y + 5) * 2 = 30. Solving gives y = 10 km/h.

A boat travels 30 km downstream in 2 hours. If the speed of the stream is 5 km/h, what is the speed of the boat in still water?

A boat travels 30 km downstream in 2 hours. If the speed of the stream is 5 km/h, what is the speed of the boat in still water?

Correct Answer: 10 km/h

Step 1: Understand that the boat travels downstream, which means it is moving with the current of the stream.
Step 2: The speed of the stream is given as 5 km/h.
Step 3: Let the speed of the boat in still water be represented as 'y' km/h.
Step 4: When the boat is going downstream, its effective speed is the speed of the boat plus the speed of the stream. This can be written as (y + 5) km/h.
Step 5: The boat travels 30 km downstream in 2 hours. We can use the formula: Distance = Speed × Time.
Step 6: Substitute the known values into the formula: 30 km = (y + 5) km/h × 2 hours.
Step 7: Simplify the equation: 30 = 2(y + 5).
Step 8: Divide both sides by 2 to isolate (y + 5): 15 = y + 5.
Step 9: Subtract 5 from both sides to solve for y: y = 15 - 5.
Step 10: Calculate y: y = 10 km/h. This is the speed of the boat in still water.

Relative Speed – Understanding how the speed of a boat is affected by the current of the stream when traveling downstream.
Algebraic Manipulation – Solving equations to find the unknown variable, in this case, the speed of the boat in still water.