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A train travels a distance of 600 km at a constant speed. If the speed of the train is increased by 5 km/hr, the journey would take 4 hrs less. Find the speed of the train.
- a)100 km/hr
- b)25 km/hr
- c)50 km/hr
- d)Cannot be determined
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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A train travels a distance of 600 km at a constant speed. If the speed...
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A train travels a distance of 600 km at a constant speed. If the speed...
Given:
Distance travelled by the train = 600 km
Let the speed of the train be 's' km/hr
To find:
The speed of the train
Solution:
We know that,
Time taken by the train to cover a distance of 600 km with a speed 's' = Distance/Speed = 600/s
If the speed of the train is increased by 5 km/hr, the new speed becomes (s+5) km/hr.
The time taken by the train to cover the same distance of 600 km with a speed of (s+5) km/hr = Distance/Speed = 600/(s+5)
According to the given condition, the journey would take 4 hours less if the speed of the train is increased by 5 km/hr.
Therefore, we have the equation:
600/s - 600/(s+5) = 4
Multiplying both sides by s(s+5), we get:
600(s+5) - 600s = 4s(s+5)
Simplifying the above equation, we get:
3000 = 4s^2 + 20s
4s^2 + 20s - 3000 = 0
Dividing both sides by 4, we get:
s^2 + 5s - 750 = 0
Solving the above quadratic equation using the quadratic formula, we get:
s = (-5 + sqrt(5^2 + 4*1*750))/(2*1) or s = (-5 - sqrt(5^2 + 4*1*750))/(2*1)
s = (-5 + 35)/2 or s = (-5 - 35)/2
s = 15 or s = -20
Since the speed of the train cannot be negative, the speed of the train is 15 km/hr.
Therefore, option B is the correct answer.
Distance travelled by the train = 600 km
Let the speed of the train be 's' km/hr
To find:
The speed of the train
Solution:
We know that,
Time taken by the train to cover a distance of 600 km with a speed 's' = Distance/Speed = 600/s
If the speed of the train is increased by 5 km/hr, the new speed becomes (s+5) km/hr.
The time taken by the train to cover the same distance of 600 km with a speed of (s+5) km/hr = Distance/Speed = 600/(s+5)
According to the given condition, the journey would take 4 hours less if the speed of the train is increased by 5 km/hr.
Therefore, we have the equation:
600/s - 600/(s+5) = 4
Multiplying both sides by s(s+5), we get:
600(s+5) - 600s = 4s(s+5)
Simplifying the above equation, we get:
3000 = 4s^2 + 20s
4s^2 + 20s - 3000 = 0
Dividing both sides by 4, we get:
s^2 + 5s - 750 = 0
Solving the above quadratic equation using the quadratic formula, we get:
s = (-5 + sqrt(5^2 + 4*1*750))/(2*1) or s = (-5 - sqrt(5^2 + 4*1*750))/(2*1)
s = (-5 + 35)/2 or s = (-5 - 35)/2
s = 15 or s = -20
Since the speed of the train cannot be negative, the speed of the train is 15 km/hr.
Therefore, option B is the correct answer.
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A train travels a distance of 600 km at a constant speed. If the speed of the train is increased by 5 km/hr, the journey would take 4 hrs less. Find the speed of the train.a)100 km/hrb)25 km/hrc)50 km/hrd)Cannot be determinede)None of theseCorrect answer is option 'B'. Can you explain this answer?
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