A boat travels 30 km upstream and 30 km downstream in a total of 8 hours. The speed of the stream is 2 km/h. What is the speed of the boat in still water?
Answer and explanation
Correct answer: 8 km/h
For a boat-and-stream problem, if x is the speed in still water, the upstream speed is x − 2 and the downstream speed is x + 2. Therefore, the time equation is 30/(x − 2) + 30/(x + 2) = 8, with x > 2. Multiplying by (x − 2)(x + 2) gives 60x = 8(x² − 4), or x² − 7.5x − 4 = 0; equivalently, 2x² − 15x − 8 = 0. Its positive solution is x = 8 (the other root is negative). Checking: 30/6 = 5 hours upstream and 30/10 = 3 hours downstream, total 8 hours. Thus option B is correct; the other choices fail this time check.
Frequently asked questions
What is the correct answer to this question?
8 km/h
Why is this the correct answer?
For a boat-and-stream problem, if x is the speed in still water, the upstream speed is x − 2 and the downstream speed is x + 2. Therefore, the time equation is 30/(x − 2) + 30/(x + 2) = 8, with x > 2. Multiplying by (x − 2)(x + 2) gives 60x = 8(x² − 4), or x² − 7.5x − 4 = 0; equivalently, 2x² − 15x − 8 = 0. Its positive solution is x = 8 (the other root is negative). Checking: 30/6 = 5 hours upstream and 30/10 = 3 hours downstream, total 8 hours. Thus option B is correct; the other choices fail this time check.
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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