A boat travels 30 km downstream in 2 hours. If the speed of the boat in still wa

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Question: A boat travels 30 km downstream in 2 hours. If the speed of the boat in still water is 12 km/h, what is the speed of the stream?

Options:

Correct Answer: 4 km/h

Solution:

Let the speed of the stream be x km/h. Downstream speed = 12 + x. Therefore, 30/(12 + x) = 2. Solving gives x = 3 km/h.

A boat travels 30 km downstream in 2 hours. If the speed of the boat in still water is 12 km/h, what is the speed of the stream?

A boat travels 30 km downstream in 2 hours. If the speed of the boat in still water is 12 km/h, what is the speed of the stream?

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 boat in still water is given as 12 km/h.
Step 3: Let the speed of the stream be x 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, which is 12 + x km/h.
Step 5: We know the boat travels 30 km downstream in 2 hours.
Step 6: Use the formula: Distance = Speed × Time. Here, Distance = 30 km and Time = 2 hours.
Step 7: Set up the equation: 30 km = (12 + x) km/h × 2 hours.
Step 8: Simplify the equation: 30 = 2(12 + x).
Step 9: Distribute the 2: 30 = 24 + 2x.
Step 10: Subtract 24 from both sides: 30 - 24 = 2x, which gives 6 = 2x.
Step 11: Divide both sides by 2 to find x: x = 3 km/h.
Step 12: Conclude that the speed of the stream is 3 km/h.

Relative Speed – Understanding how the speed of a boat changes when moving downstream or upstream due to the influence of the stream.
Algebraic Manipulation – Solving equations to find the unknown variable, in this case, the speed of the stream.