A person travels 640 km at a speed of \(x+12\) km/h in \(x\) hours. What is the travel time \(x\)?
Answer and explanation
Correct answer: 20 hours
Using distance = speed × time, we get \(x(x+12)=640\). Rearranging gives \(x^2+12x-640=0\), which factors as \((x+32)(x-20)=0\). Thus, \(x=20\) or \(x=-32\); since time cannot be negative, the valid value is 20 hours. Exam tip: For quantities such as time and distance, reject negative roots.
Frequently asked questions
What is the correct answer to this question?
20 hours
Why is this the correct answer?
Using distance = speed × time, we get \(x(x+12)=640\). Rearranging gives \(x^2+12x-640=0\), which factors as \((x+32)(x-20)=0\). Thus, \(x=20\) or \(x=-32\); since time cannot be negative, the valid value is 20 hours. Exam tip: For quantities such as time and distance, reject negative roots.
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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