Question
Quantity I: The speed of a boat in still water is 12
km/hr. It takes 4.5 hours to travel 24 km downstream and return. What is the speed of the stream? Quantity II: A boat takes 1.5 hours less to travel 36 km downstream than upstream. If the boat's speed in still water is 10 km/hr, find the speed of the stream.Solution
Solution: Quantity I: Let the speed of the stream = x km/hr. Downstream speed = (12 + x) km/hr, and upstream speed = (12 - x) km/hr. Time taken downstream = 24/(12 + x) Time taken upstream = 24/(12 - x) According to the question: 24/(12 + x) + 24/(12 - x) = 4.5 Solving for x: Cross-multiplying and simplifying, we get x = 4 km/hr. Quantity II: Let the speed of the stream = y km/hr. Downstream speed = 10 + y, and upstream speed = 10 - y. According to the question: 36/(10 - y) - 36/(10 + y) = 1.5 Solving for y: Cross-multiplying and simplifying, we get y = 2 km/hr. Answer: E (Quantity I > Quantity II)
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