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Machine A can complete a certain job in X hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete because of A's help?
- a)(x – y)/ (x + y)
- b)x / (y – x)
- c)(x + y) / xy
- d)y / (x – y)
- e)y / (x + y)
Correct answer is option 'E'. Can you explain this answer?
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Machine A can complete a certain job in X hours. Machine B can complet...
We can solve this problem as a VIC (Variable In Answer Choice) and plug in values for the two variables, x and y. Let's say x = 2 and y = 3.
Machine A can complete one job in 2 hours. Thus, the rate of Machine A is 1/2.
Machine B can complete one job in 3 hours. Thus, the rate of Machine B is 1/3.
The combined rate for Machine A and Machine B working together is: 1/2 + 1/3 = 5/6.
Using the equation (Rate)(Time) = Work, we can plug 5/6 in for the combined rate, plug 1 in for the total work (since they work together to complete 1 job), and calculate the total time as 6/5 hours.
The question asks us what fraction of the job machine B will NOT have to complete because of A's help. In other words we need to know what portion of the job machine A alone completes in that 6/5 hours.
A's rate is 1/2, and it spends 6/5 hours working. By plugging these into the RT=W formula, we calculate that, A completes (1/2)(6/5) = 3/5 of the job. Thus, machine B is saved from having to complete 3/5 of the job.
If we plug our values of x = 2 and y = 3 into the answer choices, we see that only answer choice E yields the correct value of 3/5.
Most Upvoted Answer
Machine A can complete a certain job in X hours. Machine B can complet...
The combined rate of A and B is:
1/X + 1/Y
To find the fraction of the job that B will not have to complete because of A's help, we need to determine the portion of the job that A will complete. Let's call this portion "p".
Since A and B are working together to complete the job, the combined rate is equal to the rate of the whole job, which is 1. So we can set up the equation:
1/X + 1/Y = 1
Multiplying both sides by XY, we get:
Y + X = XY
Solving for p, we get:
p = X/(X+Y)
This represents the fraction of the job that A will complete. The fraction of the job that B will not have to complete because of A's help is therefore:
1 - p = Y/(X+Y)
So the answer is (b) Y/(X+Y).
1/X + 1/Y
To find the fraction of the job that B will not have to complete because of A's help, we need to determine the portion of the job that A will complete. Let's call this portion "p".
Since A and B are working together to complete the job, the combined rate is equal to the rate of the whole job, which is 1. So we can set up the equation:
1/X + 1/Y = 1
Multiplying both sides by XY, we get:
Y + X = XY
Solving for p, we get:
p = X/(X+Y)
This represents the fraction of the job that A will complete. The fraction of the job that B will not have to complete because of A's help is therefore:
1 - p = Y/(X+Y)
So the answer is (b) Y/(X+Y).
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Machine A can complete a certain job in X hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete because of A's help?a)(x – y)/ (x + y)b)x / (y – x)c)(x + y) / xyd)y / (x – y)e)y / (x + y)Correct answer is option 'E'. Can you explain this answer?
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