A person travels a distance of 240 kilometres. If the speed is reduced by 20 kilometres per hour, the journey takes 2 hours longer. What was the person's original speed?
Answer and explanation
Correct answer: 60 kilometres per hour
Let the original speed be \(x\) kilometres per hour. The original time is \(\frac{240}{x}\) hours, while the time at the reduced speed is \(\frac{240}{x-20}\) hours. Hence, \(\frac{240}{x-20}-\frac{240}{x}=2\). On simplifying, \(x^2-20x-2400=0\), so \((x-60)(x+40)=0\). Since speed must be positive, \(x=60\) kilometres per hour. The root \(x=-40\) is not physically meaningful. Exam tip: In speed-time problems, express the times in both situations first and then form their difference.
Frequently asked questions
What is the correct answer to this question?
60 kilometres per hour
Why is this the correct answer?
Let the original speed be \(x\) kilometres per hour. The original time is \(\frac{240}{x}\) hours, while the time at the reduced speed is \(\frac{240}{x-20}\) hours. Hence, \(\frac{240}{x-20}-\frac{240}{x}=2\). On simplifying, \(x^2-20x-2400=0\), so \((x-60)(x+40)=0\). Since speed must be positive, \(x=60\) kilometres per hour. The root \(x=-40\) is not physically meaningful. Exam tip: In speed-time problems, express the times in both situations first and then form their difference.
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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