rommysingh wrote:Machine A, working alone at a constant rate, can complete a certain production lot in x hours. Machine B, working alone at a constant rate, can complete 1/5 of the same production lot in y hours. Machines A and B, working together, can complete 1/2 of the same production lot in z hours. What is the value of y in terms of x and z?
5x – 10z/2xz
2xz/5x - 10z
5xz/x + z
xz/x + z
xz/x + 2z
I knwo the solution but is there a shorter and simpler way to do it as i substitute the value into formula ab/a+b = W , this is taking a lot of time..
Let the lot = 20 units.
Let x = 5 hours.
Rate for A alone = w/t = 20/5 = 4 units per hour.
Let y = 4 hours.
This is the time for B to produce 1/5 of the lot (4 units).
Thus, B's rate = w/t = 4/4 = 1 unit per hour.
When elements work together, add their rates.
z = the time for A+B to produce 1/2 of the lot = 10/(4+1) = 2 hours.
The question asks for the value of y (4 hours). This is our target.
Now we plug x=5 and z=2 into the answers to see which yields our target of 4.
Scan the denominators.
Since 2xz = 2*5*2 = 20, the denominator in A seems too great to yield our target value of 4.
Since x+z = 5+2 = 7 and x+2z = 5 + (2*2) = 9, answer choices C, D, and E yield denominators that seem unlikely to yield our target of 4.
Answer choice
B:
(2xz)/(5x-10z) = (2*5*2)/(5*5 - 10*2) = 20/5 = 4.
The correct answer is
B.
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