A boat can cover a distance of 48 km downstream in 4 hours. If the speed of the

A boat can cover a distance of 48 km downstream in 4 hours. If the speed of the stream is 4 km/h, what is the speed of the boat in still water?

A boat can cover a distance of 48 km downstream in 4 hours. If the speed of the stream is 4 km/h, what is the speed of the boat in still water?

Correct Answer: 12 km/h

Step 1: Understand that the boat travels downstream, which means it is aided by the speed of the stream.
Step 2: The speed of the stream is given as 4 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, which is (y + 4) km/h.
Step 5: The boat covers a distance of 48 km downstream in 4 hours.
Step 6: Use the formula: Distance = Speed × Time. Here, Distance = 48 km and Time = 4 hours.
Step 7: Substitute the effective speed into the formula: 48 = (y + 4) × 4.
Step 8: Simplify the equation: 48 = 4y + 16.
Step 9: Rearrange the equation to isolate 'y': 4y = 48 - 16.
Step 10: Calculate: 4y = 32.
Step 11: Divide both sides by 4 to find 'y': y = 32 / 4.
Step 12: Calculate the final result: y = 8 km/h.

Relative Speed – Understanding how the speed of a boat changes when moving downstream or upstream, factoring in the speed of the stream.
Algebraic Manipulation – Ability to set up and solve equations based on given conditions.