A bus covers a distance of 360 km. Its speed is \(x\) km/h and its travel time is \((x-54)\) hours. What is the travel time?
Answer and explanation
Correct answer: 6 hours
Using distance = speed × time, we get \(x(x-54)=360\). Thus, \(x^2-54x-360=0\), which factors as \((x-60)(x+6)=0\). Since speed must be positive, \(x=60\) km/h. Therefore, the time is \(x-54=60-54=6\) hours. Exam tip: In speed–time problems, first form the equation distance = speed × time and reject any negative physical value.
Frequently asked questions
What is the correct answer to this question?
6 hours
Why is this the correct answer?
Using distance = speed × time, we get \(x(x-54)=360\). Thus, \(x^2-54x-360=0\), which factors as \((x-60)(x+6)=0\). Since speed must be positive, \(x=60\) km/h. Therefore, the time is \(x-54=60-54=6\) hours. Exam tip: In speed–time problems, first form the equation distance = speed × time and reject any negative physical value.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
