Worker A can complete a task alone in x days, while worker B can complete it alone in x+5 days. Together, they complete the task in 6 days. In how many days can worker A complete the task alone?
Answer and explanation
Correct answer: 10 days
The combined work rate is \(\frac{1}{6}\) of the task per day, so \(\frac{1}{x}+\frac{1}{x+5}=\frac{1}{6}\). Clearing the denominators gives \(6(2x+5)=x(x+5)\), or \(x^2-7x-30=0\). Factoring, \((x-10)(x+3)=0\), so \(x=10\) or \(x=-3\). Since a number of days cannot be negative, \(x=10\), making option B correct. Exam tip: In work-rate problems, add the reciprocals of the individual completion times.
Frequently asked questions
What is the correct answer to this question?
10 days
Why is this the correct answer?
The combined work rate is \(\frac{1}{6}\) of the task per day, so \(\frac{1}{x}+\frac{1}{x+5}=\frac{1}{6}\). Clearing the denominators gives \(6(2x+5)=x(x+5)\), or \(x^2-7x-30=0\). Factoring, \((x-10)(x+3)=0\), so \(x=10\) or \(x=-3\). Since a number of days cannot be negative, \(x=10\), making option B correct. Exam tip: In work-rate problems, add the reciprocals of the individual completion times.
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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