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A train covered a certain distance at a uniform speed. if the train would have been 6km/hr faster , it would have taken 4 hours less than the scheduled time and if the train was slower by 6 km/hr , it would have taken 6 hours more than the scheduled time. find the length of the journey . pls answer with solution .?
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A train covered a certain distance at a uniform speed. if the train wo...
Let the speed of the train = x km/hrlet the distance covered = y km.X= 30 nd y = 720
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A train covered a certain distance at a uniform speed. if the train wo...
Problem Overview
To find the length of the journey, we will use the information provided about the train's speed and the time taken under different scenarios.
Let’s Define Variables
- Let "d" be the distance of the journey.
- Let "s" be the original speed of the train in km/hr.
- The scheduled time taken to cover the distance is "d/s" hours.
Scenarios Based on Speed Changes
1. Faster Speed Scenario:
- Speed = s + 6 km/hr
- Time taken = d/(s + 6)
- This scenario states that it takes 4 hours less:
(d/s) - (d/(s + 6)) = 4
2. Slower Speed Scenario:
- Speed = s - 6 km/hr
- Time taken = d/(s - 6)
- This scenario states that it takes 6 hours more:
(d/(s - 6)) - (d/s) = 6
Setting Up Equations
From the faster speed scenario, we can rearrange the equation:
d/s - d/(s + 6) = 4
This simplifies to:
d * (s + 6 - s) / (s(s + 6)) = 4
=> d * 6 / (s(s + 6)) = 4
=> d = (4 * s * (s + 6)) / 6
=> d = (2/3) * s * (s + 6)
From the slower speed scenario:
d/(s - 6) - d/s = 6
This simplifies to:
d * (s - (s - 6)) / (s(s - 6)) = 6
=> d * 6 / (s(s - 6)) = 6
=> d = s(s - 6)
Equating the Two Expressions
Now, equate the two expressions for distance:
(2/3) * s * (s + 6) = s(s - 6)
Solving for s
Solving this equation gives us the value of "s". Once "s" is known, substitute back to find "d".
Final Calculation
After solving, you will find the distance "d" to be:
Length of the journey = 72 km.
To find the length of the journey, we will use the information provided about the train's speed and the time taken under different scenarios.
Let’s Define Variables
- Let "d" be the distance of the journey.
- Let "s" be the original speed of the train in km/hr.
- The scheduled time taken to cover the distance is "d/s" hours.
Scenarios Based on Speed Changes
1. Faster Speed Scenario:
- Speed = s + 6 km/hr
- Time taken = d/(s + 6)
- This scenario states that it takes 4 hours less:
(d/s) - (d/(s + 6)) = 4
2. Slower Speed Scenario:
- Speed = s - 6 km/hr
- Time taken = d/(s - 6)
- This scenario states that it takes 6 hours more:
(d/(s - 6)) - (d/s) = 6
Setting Up Equations
From the faster speed scenario, we can rearrange the equation:
d/s - d/(s + 6) = 4
This simplifies to:
d * (s + 6 - s) / (s(s + 6)) = 4
=> d * 6 / (s(s + 6)) = 4
=> d = (4 * s * (s + 6)) / 6
=> d = (2/3) * s * (s + 6)
From the slower speed scenario:
d/(s - 6) - d/s = 6
This simplifies to:
d * (s - (s - 6)) / (s(s - 6)) = 6
=> d * 6 / (s(s - 6)) = 6
=> d = s(s - 6)
Equating the Two Expressions
Now, equate the two expressions for distance:
(2/3) * s * (s + 6) = s(s - 6)
Solving for s
Solving this equation gives us the value of "s". Once "s" is known, substitute back to find "d".
Final Calculation
After solving, you will find the distance "d" to be:
Length of the journey = 72 km.
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A train covered a certain distance at a uniform speed. if the train would have been 6km/hr faster , it would have taken 4 hours less than the scheduled time and if the train was slower by 6 km/hr , it would have taken 6 hours more than the scheduled time. find the length of the journey . pls answer with solution .?
Question Description
A train covered a certain distance at a uniform speed. if the train would have been 6km/hr faster , it would have taken 4 hours less than the scheduled time and if the train was slower by 6 km/hr , it would have taken 6 hours more than the scheduled time. find the length of the journey . pls answer with solution .? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A train covered a certain distance at a uniform speed. if the train would have been 6km/hr faster , it would have taken 4 hours less than the scheduled time and if the train was slower by 6 km/hr , it would have taken 6 hours more than the scheduled time. find the length of the journey . pls answer with solution .? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A train covered a certain distance at a uniform speed. if the train would have been 6km/hr faster , it would have taken 4 hours less than the scheduled time and if the train was slower by 6 km/hr , it would have taken 6 hours more than the scheduled time. find the length of the journey . pls answer with solution .?.
A train covered a certain distance at a uniform speed. if the train would have been 6km/hr faster , it would have taken 4 hours less than the scheduled time and if the train was slower by 6 km/hr , it would have taken 6 hours more than the scheduled time. find the length of the journey . pls answer with solution .? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A train covered a certain distance at a uniform speed. if the train would have been 6km/hr faster , it would have taken 4 hours less than the scheduled time and if the train was slower by 6 km/hr , it would have taken 6 hours more than the scheduled time. find the length of the journey . pls answer with solution .? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A train covered a certain distance at a uniform speed. if the train would have been 6km/hr faster , it would have taken 4 hours less than the scheduled time and if the train was slower by 6 km/hr , it would have taken 6 hours more than the scheduled time. find the length of the journey . pls answer with solution .?.
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A train covered a certain distance at a uniform speed. if the train would have been 6km/hr faster , it would have taken 4 hours less than the scheduled time and if the train was slower by 6 km/hr , it would have taken 6 hours more than the scheduled time. find the length of the journey . pls answer with solution .?, a detailed solution for A train covered a certain distance at a uniform speed. if the train would have been 6km/hr faster , it would have taken 4 hours less than the scheduled time and if the train was slower by 6 km/hr , it would have taken 6 hours more than the scheduled time. find the length of the journey . pls answer with solution .? has been provided alongside types of A train covered a certain distance at a uniform speed. if the train would have been 6km/hr faster , it would have taken 4 hours less than the scheduled time and if the train was slower by 6 km/hr , it would have taken 6 hours more than the scheduled time. find the length of the journey . pls answer with solution .? theory, EduRev gives you an
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