A car covers a distance of 720 km. Its speed is \(x\) km per hour, and the time taken to cover this distance is \((x-72)\) hours. What is the speed of the car?
Answer and explanation
Correct answer: \(36+12\sqrt{14}\) km per hour
Using distance = speed × time, we get \(x(x-72)=720\), so \(x^2-72x-720=0\). Applying the quadratic formula gives \(x=36\pm12\sqrt{14}\). The negative root \(36-12\sqrt{14}\) is not a valid speed, so the speed is \(36+12\sqrt{14}\) km per hour, approximately 80.9 km per hour. Option 80 is incorrect because it would give a distance of \(80\times8=640\) km. Exam tip: Form the distance = speed × time equation first, then retain only the positive root that fits the context.
Frequently asked questions
What is the correct answer to this question?
\(36+12\sqrt{14}\) km per hour
Why is this the correct answer?
Using distance = speed × time, we get \(x(x-72)=720\), so \(x^2-72x-720=0\). Applying the quadratic formula gives \(x=36\pm12\sqrt{14}\). The negative root \(36-12\sqrt{14}\) is not a valid speed, so the speed is \(36+12\sqrt{14}\) km per hour, approximately 80.9 km per hour. Option 80 is incorrect because it would give a distance of \(80\times8=640\) km. Exam tip: Form the distance = speed × time equation first, then retain only the positive root that fits the context.
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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