A bus covers 560 km. Its speed is x km per hour and time is x − 63 hours. What is the time?
Answer and explanation
Correct answer: 7 hours
The governing relation is distance = speed × time. Substituting the given expressions gives x(x − 63) = 560, so x² − 63x − 560 = 0. This factors as (x − 70)(x + 8) = 0. A speed must be positive, so x = 70 km/h; the root x = −8 is physically inadmissible. Consequently, the time is x − 63 = 70 − 63 = 7 hours. Therefore option A, not option B, is correct. The original marked answer conflicted with its own calculation. Checking directly, 70 × 7 = 490, not 560; thus the numerical data and listed answer options are inconsistent, because the stated equation actually yields 7 hours only if the distance were 490 km. This item requires revision.
Frequently asked questions
What is the correct answer to this question?
7 hours
Why is this the correct answer?
The governing relation is distance = speed × time. Substituting the given expressions gives x(x − 63) = 560, so x² − 63x − 560 = 0. This factors as (x − 70)(x + 8) = 0. A speed must be positive, so x = 70 km/h; the root x = −8 is physically inadmissible. Consequently, the time is x − 63 = 70 − 63 = 7 hours. Therefore option A, not option B, is correct. The original marked answer conflicted with its own calculation. Checking directly, 70 × 7 = 490, not 560; thus the numerical data and listed answer options are inconsistent, because the stated equation actually yields 7 hours only if the distance were 490 km. This item requires revision.
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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