A car covers a distance of 750 km. If its speed is \(x\) km per hour and its travel time is \((x-65)\) hours, what is the speed of the car?
Answer and explanation
Correct answer: 75 km per hour
Using distance = speed × time, we get \(x(x-65)=750\). Thus, \(x^2-65x-750=0\), which factors as \((x-75)(x+10)=0\). Therefore, \(x=75\) or \(x=-10\). Since speed cannot be negative, the valid answer is 75 km per hour. In the exam, first form the quadratic equation from distance = speed × time, then reject any negative or otherwise physically invalid root.
Frequently asked questions
What is the correct answer to this question?
75 km per hour
Why is this the correct answer?
Using distance = speed × time, we get \(x(x-65)=750\). Thus, \(x^2-65x-750=0\), which factors as \((x-75)(x+10)=0\). Therefore, \(x=75\) or \(x=-10\). Since speed cannot be negative, the valid answer is 75 km per hour. In the exam, first form the quadratic equation from distance = speed × time, then reject any negative or otherwise physically invalid root.
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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