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Work/Rate

This topic has 3 expert replies and 0 member replies

Work/Rate

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It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 80 pages?

A. 12
B. 18
C. 20
D. 24
E. 30

OA is D
This question is confusing me.C an expert explain why D is the answer?

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Post
Roland2rule wrote:
It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 80 pages?

A. 12
B. 18
C. 20
D. 24
E. 30

OA is D
This question is confusing me.C an expert explain why D is the answer?
Not a bad one to back-solve.

Test B: If A can do 80 pages in 18 minutes, then we know it can do 40 pages in 9 minutes. If it takes B 4 fewer minutes to do 40 pages, then B can do 40 pages in 5 minutes.
A's rate: 40/9 = 4 4/9 = About 4.4 pages per minute.
B's rate: 40/5 = 8 pages per minute
Combined rate = About 4.4+ 8 = 12.4 pages per minute. So in 6 minutes, the two could do 12.4 * 6 pages which is greater than 70. But they should be able to do 50 pages in this time, meaning they must be working slower. If they're working slower, it must have taken A more time to do 80 pages. Eliminate A and B.

Test D: If A can do 80 pages in 24 minutes, then we know it can do 40 pages in 12 minutes. If it takes B 4 fewer minutes to do 40 pages, then B can do 40 pages in 8 minutes.
A's rate: 40/12 = 10/3 pages per minute.
B's rate: 40/8 = 5 = 15/3 pages per minute
Combined rate = 10/3 + 15/3 = 25/3 pages per minute. In 6 minutes, the two would produce 6 * (25/3) = 2*25 = 50 pages. Bingo! D is our answer.

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Post
Quote:
It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 80 pages?

A. 12
B. 18
C. 20
D. 24
E. 30

OA is D
This question is confusing me.C an expert explain why D is the answer?
Hi Roland2rule,
Let's take a look at your question.

If printer B takes 'x' minutes to print 40 pages, then printer A will take 'x+4' minutes to print 40 pages.
$$\text{Rate of Printer A}=\frac{40}{x+4}$$
$$\text{Rate of Printer B}=\frac{40}{x}$$

$$\text{Combined Rate of Printer A and B}=\frac{40}{x+4}+\frac{40}{x} ... (i)$$

The question states, "Working together, the two printers can print 50 pages in 6 minutes".
$$\text{Combined Rate of Printer A and B}=\frac{50}{6} ... (ii)$$

Equating Eq(i) and (ii)
$$\frac{40}{x+4}+\frac{40}{x} =\frac{50}{6}$$
$$\frac{40x+40\left(x+4\right)}{x\left(x+4\right)}=\frac{50}{6}$$
$$\frac{40x+40x+160}{x\left(x+4\right)}=\frac{25}{3}$$
$$40x+40x+160=\frac{25x\left(x+4\right)}{3}$$
$$80x+160=\frac{25x\left(x+4\right)}{3}$$
$$3\left(80x+160\right)=25x\left(x+4\right)$$
$$240x+480=25x^2+100x$$
$$25x^2+100x-240x-480=0$$
$$25x^2-140x-480=0$$
$$5x^2-28x-96=0$$
$$5x^2-40x+12x-96=0$$
$$5x\left(x-8\right)+12\left(x-8\right)=0$$
$$\left(5x+12\right)\left(x-8\right)=0$$
$$Either\ \left(5x+12\right)=0,\ or\ \left(x-8\right)=0$$
$$Either\ x=-\frac{12}{5},\ or\ x=8$$

Since 'x' represents the number of minutes Printer B takes to print 40 pages,so it can not be negative. Therefore we will only consider x = 8.

To print 40 pages Printer A takes = x + 4 = 8 + 4 = 24

We are asked to find the number of minutes Printer A will take to print 80 pages .
= 2 * (Number of minutes Printer A will take to print 40 pages) = 2 * ( 12) = 24 minutes

Therefore, Option D is correct.

Hope it helps.
I am available if you'd like any follow up.

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Post
Roland2rule wrote:
It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 80 pages?

A. 12
B. 18
C. 20
D. 24
E. 30

OA is D
This question is confusing me.C an expert explain why D is the answer?
Say printer B takes x minutes to print 40 pages, thus printer A would take (x + 4) minutes to print 40 pages.

We know that printer A and B together worked for 6 minutes and printed 50 pages, so let's compute the number of pages printer A and printer B would print in 6 minutes.

The number of pages printer A would print in 6 minutes = [40/(x + 4)]*6 = 240/(x + 4);
The number of pages printer B would print in 6 minutes = [40/x]*6 = 240/x

The number of pages printer A and B together would print in 6 minutes = 240/(x + 4) + 240/x

240/(x + 4) + 240/x = 50 pages (given)

=> 5x^2 - 28x - 96 = 0.

Instead of solving the unfamiliar linear equation, let's do the plug-in from the option values.

The option values are given for the time taken for printer A to print 80 pages. Since we assumed that printer A takes (x +4) minutes to print 40 pages, thus, it would take 2*(x + 4) minutes to print 80 pages. So the option values, in fact, are equal to 2(x + 4). Let's get the value of x from the options, and plug-in the equation 5x^2 - 28x - 96 = 0. If the RHS = the LHS, that option is the correct option.

A. 12: 2(x + 4) = 12 => x = 2. At x = 2, we have 5x^2 - 28x - 96 = 5*2^2 - 28*2 - 96 = 20 - 56 - 96 ≠ 0. Eliminated!
B. 18: 2(x + 4) = 18 => x = 5. At x = 5, we have 5x^2 - 28x - 96 = 5*5^2 - 28*5 - 96 = 125 - 140 - 96 ≠ 0. Eliminated!
C. 20: 2(x + 4) = 20 => x = 2. At x = 6, we have 5x^2 - 28x - 96 = 5*6^2 - 28*6 - 96 = 180 - 168 - 96 ≠ 0. Eliminated!
D. 24: 2(x + 4) = 24 => x = 2. At x = 8, we have 5x^2 - 28x - 96 = 5*8^2 - 28*8 - 96 = 320 - 224 - 96 = 320 - 320 = 0. Correct
E. 30: No need to check!

The correct answer: D

Hope this helps!

-Jay
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