Worker A alone completes a task in x days, while worker B alone completes it in (x+3) days. Together, they complete the same task in 2 days. In how many days will worker A alone complete the task?
Answer and explanation
Correct answer: 3 days
The combined work rate is \(\frac{1}{2}\) task per day, so \(\frac{1}{x}+\frac{1}{x+3}=\frac{1}{2}\). On simplifying, \(2(2x+3)=x(x+3)\), which gives \(x^2-x-6=0\). Thus, \((x-3)(x+2)=0\), so \(x=3\) or \(x=-2\). Since time cannot be negative, \(x=3\) days is valid. Exam tip: In work-rate problems, use the reciprocal of time for the rate and reject any negative time value.
Frequently asked questions
What is the correct answer to this question?
3 days
Why is this the correct answer?
The combined work rate is \(\frac{1}{2}\) task per day, so \(\frac{1}{x}+\frac{1}{x+3}=\frac{1}{2}\). On simplifying, \(2(2x+3)=x(x+3)\), which gives \(x^2-x-6=0\). Thus, \((x-3)(x+2)=0\), so \(x=3\) or \(x=-2\). Since time cannot be negative, \(x=3\) days is valid. Exam tip: In work-rate problems, use the reciprocal of time for the rate and reject any negative time value.
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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