A train covers 360 km. If its speed were 10 km/h more, it would take 3 h less. What was the original speed?
Answer and explanation
Correct answer: 30 km/h
This is a speed–time–distance word problem that leads to a quadratic equation. Let the original speed be x km/h, with x>0. The original time is 360/x hours, while the time at the increased speed is 360/(x+10) hours. Their difference is 3, so 360/x − 360/(x+10)=3. On simplifying, 3600/[x(x+10)]=3, giving x²+10x−1200=0. Factoring gives (x−30)(x+40)=0. Since speed cannot be negative, x=30 km/h. Checking: 360/30=12 hours and 360/40=9 hours, a reduction of exactly 3 hours. Therefore option A is correct; the other positive choices do not satisfy the stated time difference.
Frequently asked questions
What is the correct answer to this question?
30 km/h
Why is this the correct answer?
This is a speed–time–distance word problem that leads to a quadratic equation. Let the original speed be x km/h, with x>0. The original time is 360/x hours, while the time at the increased speed is 360/(x+10) hours. Their difference is 3, so 360/x − 360/(x+10)=3. On simplifying, 3600/[x(x+10)]=3, giving x²+10x−1200=0. Factoring gives (x−30)(x+40)=0. Since speed cannot be negative, x=30 km/h. Checking: 360/30=12 hours and 360/40=9 hours, a reduction of exactly 3 hours. Therefore option A is correct; the other positive choices do not satisfy the stated time 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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