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.

Could someone explain how to do this problem below? When I originally attempted it, the formula that ran through my head was a x b/a + b. But do you not use that because it is not asking for the combined total rate?

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?

A. 5x-10z/2xz
B. 2xz/5x-10z
C. 5xz/x+z
D. xz/x+z
E. xz/x+2z

The a*b/(a+b) formula implies that 'a' is the time required for one entity to complete a job and 'b' is the time for another entity to complete the job.

A: can complete the job in x hours.
B: if it can complete 1/5 of the job in y hours, then it completes the whole job in 5y hours.
Together: If they complete half the job in z hours, then they can complete the whole job in 2z hours

Summary: A: = x hours; B = 5y hours; Together = 2z hours. Using our trusty formula, we get (x * 5y)/ (x + 5y) = 2z

x * 5y = (x + 5y) * 2z
5xy = 2zx + 10zy
5xy - 10zy = 2zx
y(5x - 10z) = 2zx
y = 2zx/(5x - 10z) -- answer is B