A bus covers a distance of 990 km. Its speed is \(x\) km/h and its travel time is \((x-89)\) hours. How much time will the bus take to cover the distance?
Answer and explanation
Correct answer: 10 hours
Using distance = speed × time, we get \(x(x-89)=990\). Thus, \(x^2-89x-990=0\), which factors as \((x-99)(x+10)=0\). Since speed must be positive, \(x=99\) km/h; the root \(x=-10\) is not physically meaningful. Therefore, the time is \(x-89=99-89=10\) hours. Exam tip: In speed–time problems, first use \(D=S\times T\), then reject any negative value that is not physically meaningful.
Frequently asked questions
What is the correct answer to this question?
10 hours
Why is this the correct answer?
Using distance = speed × time, we get \(x(x-89)=990\). Thus, \(x^2-89x-990=0\), which factors as \((x-99)(x+10)=0\). Since speed must be positive, \(x=99\) km/h; the root \(x=-10\) is not physically meaningful. Therefore, the time is \(x-89=99-89=10\) hours. Exam tip: In speed–time problems, first use \(D=S\times T\), then reject any negative value that is not physically meaningful.
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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