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A train travels a distance of 250 km at a uniform speed. If the speed has been 5 km / h less, then it would have taken 5/2 hours more to cover the same distance. find the speed of train?
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A train travels a distance of 250 km at a uniform speed. If the speed ...
To find the speed of the train, we can use the information provided about the distance, speed, and time taken. Let’s break it down step by step.
Step 1: Define Variables
- Let the speed of the train be \( x \) km/h.
- The time taken to travel 250 km at speed \( x \) is given by the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{250}{x} \]
Step 2: Adjusted Speed and Time
- If the speed is 5 km/h less, the new speed becomes \( (x - 5) \) km/h.
- The time taken at this new speed is:
\[ \text{Time} = \frac{250}{x - 5} \]
Step 3: Set Up the Equation
- According to the problem, the difference in time taken when the speed is reduced by 5 km/h is \( \frac{5}{2} \) hours:
\[ \frac{250}{x - 5} - \frac{250}{x} = \frac{5}{2} \]
Step 4: Solve the Equation
- Multiply through by \( 2x(x - 5) \) to eliminate the denominators:
\[ 500x - 500(x - 5) = 5x(x - 5) \]
- This simplifies to:
\[ 500x - 500x + 2500 = 5x^2 - 25x \]
- Rearranging gives:
\[ 5x^2 - 25x - 2500 = 0 \]
- Dividing the whole equation by 5:
\[ x^2 - 5x - 500 = 0 \]
Step 5: Factor or Use Quadratic Formula
- The quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) where \( a=1, b=-5, c=-500 \):
\[ x = \frac{5 \pm \sqrt{25 + 2000}}{2} \]
\[ x = \frac{5 \pm 45}{2} \]
- This gives two possible solutions:
\[ x = 25 \] (valid speed)
\[ x = -20 \] (not valid)
Conclusion: Speed of the Train
- Thus, the speed of the train is **25 km/h**.
Step 1: Define Variables
- Let the speed of the train be \( x \) km/h.
- The time taken to travel 250 km at speed \( x \) is given by the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{250}{x} \]
Step 2: Adjusted Speed and Time
- If the speed is 5 km/h less, the new speed becomes \( (x - 5) \) km/h.
- The time taken at this new speed is:
\[ \text{Time} = \frac{250}{x - 5} \]
Step 3: Set Up the Equation
- According to the problem, the difference in time taken when the speed is reduced by 5 km/h is \( \frac{5}{2} \) hours:
\[ \frac{250}{x - 5} - \frac{250}{x} = \frac{5}{2} \]
Step 4: Solve the Equation
- Multiply through by \( 2x(x - 5) \) to eliminate the denominators:
\[ 500x - 500(x - 5) = 5x(x - 5) \]
- This simplifies to:
\[ 500x - 500x + 2500 = 5x^2 - 25x \]
- Rearranging gives:
\[ 5x^2 - 25x - 2500 = 0 \]
- Dividing the whole equation by 5:
\[ x^2 - 5x - 500 = 0 \]
Step 5: Factor or Use Quadratic Formula
- The quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) where \( a=1, b=-5, c=-500 \):
\[ x = \frac{5 \pm \sqrt{25 + 2000}}{2} \]
\[ x = \frac{5 \pm 45}{2} \]
- This gives two possible solutions:
\[ x = 25 \] (valid speed)
\[ x = -20 \] (not valid)
Conclusion: Speed of the Train
- Thus, the speed of the train is **25 km/h**.
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A train travels a distance of 250 km at a uniform speed. If the speed has been 5 km / h less, then it would have taken 5/2 hours more to cover the same distance. find the speed of train?
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A train travels a distance of 250 km at a uniform speed. If the speed has been 5 km / h less, then it would have taken 5/2 hours more to cover the same distance. find the speed of train? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A train travels a distance of 250 km at a uniform speed. If the speed has been 5 km / h less, then it would have taken 5/2 hours more to cover the same distance. find the speed of train? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A train travels a distance of 250 km at a uniform speed. If the speed has been 5 km / h less, then it would have taken 5/2 hours more to cover the same distance. find the speed of train?.
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