Machine x & y

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Machine x & y

by Amrabdelnaby » Tue Jan 05, 2016 10:48 am
Dear Pros,

Could you please tell me if I did the calculations right? even though I got the answer right, but I just want to make sure that my thinking is also right.

Machines X and Y produced identical bottles at different constant rates. Machine X operating alone for 4 hours filled part of a production lot; then machine y operating alone for 3 hours filled the rest of this lot. How many hours would it have taken machine X operating alone to fill the entire production lot?

1) Machine X produced 30 bottles per minute

2) Machine X produced as twice as many bottles in 4 hours as Machine Y produced in 3 hours.

statement 1 is insufficient

as for statement 2:

lets call time T, output O, and rate R

Tx = 4 --> Ox = 2x --> Rx = 2x/4 = x/2
Ty = 3 --> Oy = x --> Ry = x/3

total output is 3x

Tx to fill the lot alone = 3x/(x/2) = 6x/x = 6 hours

hence sufficient.

Am I right?

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by MartyMurray » Tue Jan 05, 2016 3:06 pm
Amrabdelnaby wrote:Dear Pros,

Could you please tell me if I did the calculations right? even though I got the answer right, but I just want to make sure that my thinking is also right.
Yes, your thinking is correct.

At the same time, you didn't need to do as much. For one thing, y's rate does not matter. All that matters is that the lot = 1.5 * (x's 4 hour production). So for x to complete the entire lot would take 1.5 * 4 = 6 hours.
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by Matt@VeritasPrep » Fri Jan 08, 2016 1:43 pm
I'd think of it this way:

Lot = 4x + 3y

S1:: x = 30
S2:: 4x = 2*(3y)

Since S2 gives you 4x = 6y, you know that 3y = 2x. So we could also write Lot = 4x + 2x, and we're set.