A train covers a distance of 300 kilometres. If its speed is increased by 10 kilometres per hour, the travel time decreases by 1 hour. What was the original speed of the train?
Answer and explanation
Correct answer: 50 kilometres per hour
Let the original speed be \(x\) kilometres per hour. The decrease in time gives \(\frac{300}{x}-\frac{300}{x+10}=1\). Simplifying, \(x^2+10x-3000=0\), which factors as \((x-50)(x+60)=0\). Since speed must be positive, \(x=50\) kilometres per hour. In such problems, always reject the negative root as physically meaningless.
Frequently asked questions
What is the correct answer to this question?
50 kilometres per hour
Why is this the correct answer?
Let the original speed be \(x\) kilometres per hour. The decrease in time gives \(\frac{300}{x}-\frac{300}{x+10}=1\). Simplifying, \(x^2+10x-3000=0\), which factors as \((x-50)(x+60)=0\). Since speed must be positive, \(x=50\) kilometres per hour. In such problems, always reject the negative root as physically meaningless.
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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