Problem Solving

Fdelpesce wrote: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

Here's the algebraic solution:

Determine the rates per hour.

Rate = output/time

Machine A, working alone at a constant rate, can complete a certain production lot in x hours.
Output = 1 lot
Time = x hours
So, hourly rate = 1/x lots per hour

Machine B, working alone at a constant rate, can complete 1/5 of the same production lot in y hours.
Output = 1/5 lots
Time = y hours
So, hourly rate = (1/5)/y lots per hour
= 1/(5y) lots per hour

Machines A and B, working together, can complete 1/2 of the same production lot in z hours.
Output = 1/2 lots
Time = z hours
So, hourly rate = (1/2)/z lots per hour
= 1/(2z) lots per hour

IMPORTANT: the hourly rate for machine A + the hourly rate for machine B = combined hourly rate for A and B
So, 1/x + 1/(5y) = 1/(2z) . . . solve for y
Multiply both sides by 10xyz to get: 10yz + 2xz = 5xy
Rearrange to get: 2xz = 5xy - 10yz
Factor right side to get: 2xz = y(5x - 10z)
Isolate y to get: 2xz/(5x - 10z) = y

Answer = B

Cheers,
Brent

Hey Chiccufrazer,

Actually this would certainly be considered a hard question (7-800). Most GMAT explanations look very straightforward in retrospect, but both plugging in and algebra here are pretty time-consuming, with lots of steps where one could make a mistake.

-t