A bus covers a distance of 1056 km. If its speed is \(x\) km/h and its travel time is \((x-85)\) hours, how much time does it take to complete the journey?
Answer and explanation
Correct answer: 11 hours
Using distance = speed × time, \(x(x-85)=1056\), so \(x^2-85x-1056=0\). Factoring gives \((x-96)(x+11)=0\), hence \(x=96\) or \(x=-11\). Speed cannot be negative, so \(x=96\) km/h. Therefore, the time is \(x-85=96-85=11\) hours. Exam tip: In speed–time–distance problems, first write \(D=ST\) and reject any negative value that is physically impossible.
Frequently asked questions
What is the correct answer to this question?
11 hours
Why is this the correct answer?
Using distance = speed × time, \(x(x-85)=1056\), so \(x^2-85x-1056=0\). Factoring gives \((x-96)(x+11)=0\), hence \(x=96\) or \(x=-11\). Speed cannot be negative, so \(x=96\) km/h. Therefore, the time is \(x-85=96-85=11\) hours. Exam tip: In speed–time–distance problems, first write \(D=ST\) and reject any negative value that is physically impossible.
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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