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The speed of a locomotive without any wagons attached to it is 40kmph.It diminishes by a quantity which is proportional to the cube root of the number of wagons attached.If the speed of the locomotive is 34kmph when 27 wagons are attached,what is the maximum number of wagons that can be attached if the condition is that the speed should not fall below 30kmph?
Verified Answer
The speed of a locomotive without any wagons attached to it is 40kmph....
To find the maximum number of wagons that can be attached to the locomotive, we need to find the value of "x" in the following equation:
40 - k * x^(1/3) = 30
where "k" is the proportionality constant.
We can first find the value of "k" by substituting the known values for the number of wagons and the corresponding speed:
k = (40 - 34) / 27^(1/3) = 0.24
Substituting this value of "k" into the equation above, we get:
40 - 0.24 * x^(1/3) = 30
Solving for "x," we find that the maximum number of wagons that can be attached to the locomotive is approximately 57.
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Most Upvoted Answer
The speed of a locomotive without any wagons attached to it is 40kmph....
Problem: Find the maximum number of wagons that can be attached to a locomotive without reducing its speed below 30kmph.
Given:
- Speed of the locomotive without any wagons = 40kmph
- Speed diminishes by a quantity proportional to the cube root of the number of wagons attached
- Speed of the locomotive with 27 wagons attached = 34kmph
Approach:
1. Use the given information to find the proportionality constant.
2. Use the proportionality constant to form an equation relating the speed and the number of wagons attached.
3. Solve the equation to find the maximum number of wagons that can be attached without reducing the speed below 30kmph.
Solution:
1. Let the proportionality constant be k. Then, we have:
- k = (40 - 34) / (27^(1/3))
- k = 1.246
2. Let S be the speed of the locomotive with n wagons attached. Then, we have:
- S = 40 - k * (n^(1/3))
3. To find the maximum number of wagons that can be attached without reducing the speed below 30kmph, we need to solve the equation:
- 30 = 40 - k * (n^(1/3))
- k * (n^(1/3)) = 10
- n^(1/3) = 10 / k
- n = (10 / k)^3
- n = 669
Therefore, the maximum number of wagons that can be attached to the locomotive without reducing its speed below 30kmph is 669.
Given:
- Speed of the locomotive without any wagons = 40kmph
- Speed diminishes by a quantity proportional to the cube root of the number of wagons attached
- Speed of the locomotive with 27 wagons attached = 34kmph
Approach:
1. Use the given information to find the proportionality constant.
2. Use the proportionality constant to form an equation relating the speed and the number of wagons attached.
3. Solve the equation to find the maximum number of wagons that can be attached without reducing the speed below 30kmph.
Solution:
1. Let the proportionality constant be k. Then, we have:
- k = (40 - 34) / (27^(1/3))
- k = 1.246
2. Let S be the speed of the locomotive with n wagons attached. Then, we have:
- S = 40 - k * (n^(1/3))
3. To find the maximum number of wagons that can be attached without reducing the speed below 30kmph, we need to solve the equation:
- 30 = 40 - k * (n^(1/3))
- k * (n^(1/3)) = 10
- n^(1/3) = 10 / k
- n = (10 / k)^3
- n = 669
Therefore, the maximum number of wagons that can be attached to the locomotive without reducing its speed below 30kmph is 669.
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The speed of a locomotive without any wagons attached to it is 40kmph.It diminishes by a quantity which is proportional to the cube root of the number of wagons attached.If the speed of the locomotive is 34kmph when 27 wagons are attached,what is the maximum number of wagons that can be attached if the condition is that the speed should not fall below 30kmph?
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The speed of a locomotive without any wagons attached to it is 40kmph.It diminishes by a quantity which is proportional to the cube root of the number of wagons attached.If the speed of the locomotive is 34kmph when 27 wagons are attached,what is the maximum number of wagons that can be attached if the condition is that the speed should not fall below 30kmph? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The speed of a locomotive without any wagons attached to it is 40kmph.It diminishes by a quantity which is proportional to the cube root of the number of wagons attached.If the speed of the locomotive is 34kmph when 27 wagons are attached,what is the maximum number of wagons that can be attached if the condition is that the speed should not fall below 30kmph? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The speed of a locomotive without any wagons attached to it is 40kmph.It diminishes by a quantity which is proportional to the cube root of the number of wagons attached.If the speed of the locomotive is 34kmph when 27 wagons are attached,what is the maximum number of wagons that can be attached if the condition is that the speed should not fall below 30kmph?.
The speed of a locomotive without any wagons attached to it is 40kmph.It diminishes by a quantity which is proportional to the cube root of the number of wagons attached.If the speed of the locomotive is 34kmph when 27 wagons are attached,what is the maximum number of wagons that can be attached if the condition is that the speed should not fall below 30kmph? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The speed of a locomotive without any wagons attached to it is 40kmph.It diminishes by a quantity which is proportional to the cube root of the number of wagons attached.If the speed of the locomotive is 34kmph when 27 wagons are attached,what is the maximum number of wagons that can be attached if the condition is that the speed should not fall below 30kmph? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The speed of a locomotive without any wagons attached to it is 40kmph.It diminishes by a quantity which is proportional to the cube root of the number of wagons attached.If the speed of the locomotive is 34kmph when 27 wagons are attached,what is the maximum number of wagons that can be attached if the condition is that the speed should not fall below 30kmph?.
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