A boat travels 40 km downstream and 24 km upstream in the same time. The speed in still water is 8 km/h more than the speed of the stream. What is the speed of the stream?
Answer and explanation
Correct answer: 4 km/h
Let the stream speed be x km/h. Then the speed in still water is x + 8 km/h. The downstream speed is x + 8 + x = 2x + 8, and the upstream speed is x + 8 − x = 8 km/h. Since the two travel times are equal, 40/(2x + 8) = 24/8 = 3. Therefore 40 = 3(2x + 8), so 40 = 6x + 24 and x = 16/6 = 8/3 km/h, which does not match the supplied options. Thus the item as written is inconsistent: option B = 4 km/h would give downstream time 40/16 = 2.5 h and upstream time 24/8 = 3 h, not equal. No option is mathematically correct under the stated data.
Frequently asked questions
What is the correct answer to this question?
4 km/h
Why is this the correct answer?
Let the stream speed be x km/h. Then the speed in still water is x + 8 km/h. The downstream speed is x + 8 + x = 2x + 8, and the upstream speed is x + 8 − x = 8 km/h. Since the two travel times are equal, 40/(2x + 8) = 24/8 = 3. Therefore 40 = 3(2x + 8), so 40 = 6x + 24 and x = 16/6 = 8/3 km/h, which does not match the supplied options. Thus the item as written is inconsistent: option B = 4 km/h would give downstream time 40/16 = 2.5 h and upstream time 24/8 = 3 h, not equal. No option is mathematically correct under the stated data.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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