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Machines X and Y pack books continuously, each working at a constant 15 Jun 2021, 08:45
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Machines X and Y pack books continuously, each working at a constant rate, but Machine Y works 50% faster than Machine X. If Machine Y packs 48,000 more books in a 24-hour period than Machine X does, what is Machine X’s packing rate in books per hour?

(A) 4,000
(B) 6,000
(C) 8,000
(D) 12,000
(E) 16,000
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Machines X and Y pack books continuously, each working at a constant 15 Jun 2021, 08:57
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rate per hour of machine X = a
and that of b = 1.5a
given Machine Y packs 48,000 more books in a 24-hour period than Machine X does
24*(1.5a-a)=48000
a = 4000
option A

Bunuel
Machines X and Y pack books continuously, each working at a constant rate, but Machine Y works 50% faster than Machine X. If Machine Y packs 48,000 more books in a 24-hour period than Machine X does, what is Machine X’s packing rate in books per hour?

(A) 4,000
(B) 6,000
(C) 8,000
(D) 12,000
(E) 16,000
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Machines X and Y pack books continuously, each working at a constant 15 Jun 2021, 09:19
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What helps me in solving these questions is to keep in mind:
What value do I ultimately want?. The answer to that in this case is books per hour.

That’s step 1.

Step 2: Find books per hour for Y: That would be 2,000 more books than X.
The more is important here.

Step 3: Y is 1.5 times as efficient as X. This means,
If X produces x books, Y produces 1.5x books or 1.5x-1x = 0.5x more

So, 0.5x = 2000; x will pack 4K books
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Machines X and Y pack books continuously, each working at a constant 16 Jun 2021, 04:31
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For work problems a good approach is to utilize the following equation for starters: Rate * Time = Work.

Since we have two machines with different rates, lets map down what information we have

Rate X: x
Rate Y: x*1.5
Hours X and Y: 24
Work X: x*24
Work Y: x*24 + 48,000

I can think of two different ways of approaching this question, using mostly the same calculations but different thought processes.

Fill out the equation for Machine Y and solve for x
x*1.5 * 24 = 24x + 48,000
Divide by 24
x*1.5 = x + 2,000
Subtract x
x*0.5 = 2,000
Multiply by 2
x = 4,000

Calculate the difference
We know that the "Work" for X is x * 24 and "Work" for Y is x * 24 + 48,000. If we subtract Work for X from Work from Y we get the following:
Difference = x * 24 + 48,000- x*24 = 48,000
We also know that this is the difference per 24 hours, so lets divide by 24 to get the difference per hour
Difference per hour = 48,000 / 24 = 2,000
The difference per hour is the same as the rate for Y - the rate for X, which we defined before we started solving the question.
1.5x - x = 0.5x = 2,000
Now we just multiply this by two to get x.
0,5x*2 = x = 2,000 * 2 = 4,000
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Machines X and Y pack books continuously, each working at a constant 26 Dec 2024, 19:33
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