A car covers a distance of 800 km. If its speed is \(x\) km/h and its travel time is \((x-92)\) hours, what is the speed of the car?
Answer and explanation
Correct answer: 100 km per hour
Using distance = speed × time, we get \(x(x-92)=800\). Thus, \(x^2-92x-800=0\), which factors as \((x-100)(x+8)=0\). Therefore, \(x=100\) or \(x=-8\). Since speed cannot be negative, the valid speed is 100 km per hour. In such problems, always reject a negative root when it has no physical meaning.
Frequently asked questions
What is the correct answer to this question?
100 km per hour
Why is this the correct answer?
Using distance = speed × time, we get \(x(x-92)=800\). Thus, \(x^2-92x-800=0\), which factors as \((x-100)(x+8)=0\). Therefore, \(x=100\) or \(x=-8\). Since speed cannot be negative, the valid speed is 100 km per hour. In such problems, always reject a negative root when it has no physical meaning.
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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