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Working independently, Machine A can complete a work in 3.5 hours, while Machine B can complete the same work in x hours. Working simultaneously, they together complete the same work in 1.5 hours.
Quantity A
3
Quantity B
x
3
Quantity B
x
- a)Quantity A is greater.
- b)Quantity B is greater.
- c)The two quantities are equal.
- d)The relationship cannot be determined from the information given.
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Working independently, Machine A can complete a work in 3.5 hours, whi...
To determine the relationship between the two quantities, let's first find the rates at which each machine completes the work.
Machine A completes the work in 3.5 hours, so its rate can be calculated as:
Rate of Machine A = 1 work / 3.5 hours = 2/7 work per hour
Machine B completes the work in x hours, so its rate can be calculated as:
Rate of Machine B = 1 work / x hours = 1/x work per hour
To find the combined rate when both machines work simultaneously, we can add their individual rates:
Combined rate = Rate of Machine A + Rate of Machine B
= 2/7 + 1/x work per hour
Since they complete the work together in 1.5 hours, we can calculate the combined rate using the formula:
Combined rate = 1 work / 1.5 hours
= 2/3 work per hour
Now, equating the combined rate to the sum of individual rates, we have:
2/3 = 2/7 + 1/x
To solve for x, we can simplify the equation by finding a common denominator. In this case, the common denominator is 7x:
14x/21 = 6x/21 + 7/7x
Multiplying both sides by 21x to eliminate the denominators:
14x^2 = 6x + 21
Simplifying the equation further:
14x^2 - 6x - 21 = 0
Now, we can solve this quadratic equation to find the value of x. However, the exact value of x is not necessary to determine the relationship between the quantities.
Since Machine A completes the work in 3.5 hours, which is less than any possible value of x, the quantity A (3) is greater than quantity B (x) for all positive values of x. Therefore, the correct answer is option A: Quantity A is greater.
Machine A completes the work in 3.5 hours, so its rate can be calculated as:
Rate of Machine A = 1 work / 3.5 hours = 2/7 work per hour
Machine B completes the work in x hours, so its rate can be calculated as:
Rate of Machine B = 1 work / x hours = 1/x work per hour
To find the combined rate when both machines work simultaneously, we can add their individual rates:
Combined rate = Rate of Machine A + Rate of Machine B
= 2/7 + 1/x work per hour
Since they complete the work together in 1.5 hours, we can calculate the combined rate using the formula:
Combined rate = 1 work / 1.5 hours
= 2/3 work per hour
Now, equating the combined rate to the sum of individual rates, we have:
2/3 = 2/7 + 1/x
To solve for x, we can simplify the equation by finding a common denominator. In this case, the common denominator is 7x:
14x/21 = 6x/21 + 7/7x
Multiplying both sides by 21x to eliminate the denominators:
14x^2 = 6x + 21
Simplifying the equation further:
14x^2 - 6x - 21 = 0
Now, we can solve this quadratic equation to find the value of x. However, the exact value of x is not necessary to determine the relationship between the quantities.
Since Machine A completes the work in 3.5 hours, which is less than any possible value of x, the quantity A (3) is greater than quantity B (x) for all positive values of x. Therefore, the correct answer is option A: Quantity A is greater.
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Community Answer
Working independently, Machine A can complete a work in 3.5 hours, whi...
Given:
- Machine A working ALONE can complete a work in 3.5 hours
- Machine B working ALONE can complete the same work in x hours
- Machine A & B working together can complete the same work in 1.5 hours
We have to find the value of x and compare it with 3.
The part of work Machine A working ALONE completes in one hour = 1/.35 = 2/7
The part of work Machine B working ALONE completes in one hour = 1/x
Thus, the part of work Machine A & B working together completes in one hour
x = 2.625 hours.
Thus, Quantity A (=3) is greater than Quantity B (= x = 2.625).
The part of work Machine A working ALONE completes in one hour = 1/.35 = 2/7
The part of work Machine B working ALONE completes in one hour = 1/x
Thus, the part of work Machine A & B working together completes in one hour
x = 2.625 hours.
Thus, Quantity A (=3) is greater than Quantity B (= x = 2.625).
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Working independently, Machine A can complete a work in 3.5 hours, while Machine B can complete the same work in x hours. Working simultaneously, they together complete the same work in 1.5 hours.Quantity A3Quantity Bxa)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'A'. Can you explain this answer?
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