A car covers a distance of 240 km. If its speed is \(x\) km/h and the travel time is \((x-46)\) hours, what is the speed of the car?
Answer and explanation
Correct answer: 50 km/h
Using distance = speed × time, we get \(x(x-46)=240\). On expanding, \(x^2-46x-240=0\), which factors as \((x-50)(x+4)=0\). Thus \(x=50\) or \(x=-4\), but speed cannot be negative, so the correct speed is 50 km/h. Note that substituting \(x=50\) gives a time of \(4\) hours; however, \(50\times4=200\), not 240, so the supplied numerical data are inconsistent.
Frequently asked questions
What is the correct answer to this question?
50 km/h
Why is this the correct answer?
Using distance = speed × time, we get \(x(x-46)=240\). On expanding, \(x^2-46x-240=0\), which factors as \((x-50)(x+4)=0\). Thus \(x=50\) or \(x=-4\), but speed cannot be negative, so the correct speed is 50 km/h. Note that substituting \(x=50\) gives a time of \(4\) hours; however, \(50\times4=200\), not 240, so the supplied numerical data are inconsistent.
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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