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It takes printer A 4 more minutes more than printer B to [#permalink]
21 Feb 2007, 03:53

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

56% (04:34) correct
44% (03:37) wrong based on 68 sessions

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?

My answer is D.
Did it by picking the answer first and testing it.... Did not take very long....

We start the other way round. We say that printer A can print 80 pages in 24 minutes, then we can imply its rate:

r*24=80
r=80/24=10/3

Then, we test this rate to determine how many minutes it will take to print 40 pages:

10/3*t=40
t=12 minutes

Then printer B must have printed 40 pages in 8 minutes. Knowing this, we can determine the implied rate of B.

r*8=40
r=40/8=5

Now calculate the common rate: 10/3+5=25/3
And test it whether it works with the stated evidence, that those two printers working together can print 50 pages in 6 minutes:

25/3*6=50... it does work.

I started the values from choice C, after that you know which way to go, up or down
SO maximum you have to test two values.

Last edited by SimaQ on 21 Feb 2007, 05:33, edited 1 time in total.

Re: Printer Work Problem [#permalink]
21 Feb 2007, 05:32

2

This post received KUDOS

bz9 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

If it takes 4 more minutes for A to print 40 pages than it takes B,
it takes 5 more minutes for A to print 50 pages than it takes B.

Thus if b is the number of minutes than B takes to print 50 pages,
we can write:

1/b+1/(b+5)=1/6 (since in 1 minute, they print 1/6th of the 50 page job)

6(2b+5)=b(b+5)

b^2-7b-30=0
(b-10)(b+3)=0

b=10

Thus it takes A 15 minutes to print 50 pages and 15*80/50=24 minutes to print 80 pages

It is easy to pick the answers and make the back solving, but the direct solve would be:

A => 40/(T+4) pg/min
B => 40/T pg/min
A+B => 50/6 pg/min

So: 40/(T+4) + 40/T = 50/6
with some algebra (T-8)*(5T+12)=0 so T=8min or T=-12/5min
Taking the T=8, A makes 40 pages in 12 min (8+4), and would take then 24 min to make 80pgs.

Re: Printer Work Problem [#permalink]
20 Mar 2012, 13:23

kevincan wrote:

bz9 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

If it takes 4 more minutes for A to print 40 pages than it takes B, it takes 5 more minutes for A to print 50 pages than it takes B.

Thus if b is the number of minutes than B takes to print 50 pages, we can write:

1/b+1/(b+5)=1/6 (since in 1 minute, they print 1/6th of the 50 page job)

6(2b+5)=b(b+5)

b^2-7b-30=0 (b-10)(b+3)=0

b=10

Thus it takes A 15 minutes to print 50 pages and 15*80/50=24 minutes to print 80 pages

Kevin,

Would you please show me how you arrive 'If it takes 4 more minutes for A to print 40 pages than it takes B, it takes 5 more minutes for A to print 50 pages than it takes B.'?

Re: Printer Work Problem [#permalink]
20 Mar 2012, 13:32

Expert's post

Minhphuoc wrote:

kevincan wrote:

bz9 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

If it takes 4 more minutes for A to print 40 pages than it takes B, it takes 5 more minutes for A to print 50 pages than it takes B.

Thus if b is the number of minutes than B takes to print 50 pages, we can write:

1/b+1/(b+5)=1/6 (since in 1 minute, they print 1/6th of the 50 page job)

6(2b+5)=b(b+5)

b^2-7b-30=0 (b-10)(b+3)=0

b=10

Thus it takes A 15 minutes to print 50 pages and 15*80/50=24 minutes to print 80 pages

Kevin,

Would you please show me how you arrive 'If it takes 4 more minutes for A to print 40 pages than it takes B, it takes 5 more minutes for A to print 50 pages than it takes B.'?

Thanks Phuoc

4 more minutes to print 40 pages --> in 1 more minutes 40/4=10 pages --> so in 5 more minutes 5*10 pages.

Complete solution: It takes printer A 4 more minutes 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

Let the time needed to print 40 pages for printer A be \(a\) minutes, so for printer B it would be \(a-4\) minutes.

The rate of A would be \(rate=\frac{job}{time}=\frac{40}{a}\) pages per minute and the rate of B \(rate=\frac{job}{time}=\frac{40}{a-4}\) pages per minute.

Their combined rate would be \(\frac{40}{a}+\frac{40}{a-4}\) pages per minute. Also as "two printers can print 50 pages in 6 minutes" then their combined rate is \(rate=\frac{job}{time}=\frac{50}{6}\), so \(\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}\).

\(\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}\) --> \(\frac{1}{a}+\frac{1}{a-4}=\frac{5}{24}\). At this point we can either try to substitute the values from answer choices or solve quadratic equation. Remember as we are asked to find time needed for printer A to print \(80\) pages, then the answer would be \(2a\) (as \(a\) is the time needed to print \(40\) pages). Answer D works: \(2a=24\) --> \(a=12\) --> \(\frac{1}{12}+\frac{1}{8}=\frac{5}{24}\).

Re: Printer Work Problem [#permalink]
21 Mar 2012, 07:36

Thank you, Bunuel.

Bunuel wrote:

Minhphuoc wrote:

kevincan 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

If it takes 4 more minutes for A to print 40 pages than it takes B, it takes 5 more minutes for A to print 50 pages than it takes B.

Thus if b is the number of minutes than B takes to print 50 pages, we can write:

1/b+1/(b+5)=1/6 (since in 1 minute, they print 1/6th of the 50 page job)

6(2b+5)=b(b+5)

b^2-7b-30=0 (b-10)(b+3)=0

b=10

Thus it takes A 15 minutes to print 50 pages and 15*80/50=24 minutes to print 80 pages

Kevin,

Would you please show me how you arrive 'If it takes 4 more minutes for A to print 40 pages than it takes B, it takes 5 more minutes for A to print 50 pages than it takes B.'?

Thanks Phuoc

4 more minutes to print 40 pages --> in 1 more minutes 40/4=10 pages --> so in 5 more minutes 5*10 pages.

Complete solution: It takes printer A 4 more minutes 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

Let the time needed to print 40 pages for printer A be \(a\) minutes, so for printer B it would be \(a-4\) minutes.

The rate of A would be \(rate=\frac{job}{time}=\frac{40}{a}\) pages per minute and the rate of B \(rate=\frac{job}{time}=\frac{40}{a-4}\) pages per minute.

Their combined rate would be \(\frac{40}{a}+\frac{40}{a-4}\) pages per minute. Also as "two printers can print 50 pages in 6 minutes" then their combined rate is \(rate=\frac{job}{time}=\frac{50}{6}\), so \(\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}\).

\(\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}\) --> \(\frac{1}{a}+\frac{1}{a-4}=\frac{5}{24}\). At this point we can either try to substitute the values from answer choices or solve quadratic equation. Remember as we are asked to find time needed for printer A to print \(80\) pages, then the answer would be \(2a\) (as \(a\) is the time needed to print \(40\) pages). Answer D works: \(2a=24\) --> \(a=12\) --> \(\frac{1}{12}+\frac{1}{8}=\frac{5}{24}\).

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