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Some Work problems: how to solve these algebraically?

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Some Work problems: how to solve these algebraically? [#permalink] New post 23 May 2010, 20:14
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (01:18) wrong based on 4 sessions
Hi all,

I have a couple questions regarding the work problems below. I know how to solve these through plugging in numbers or using the answer choices, but how would you solve these algebraically?

1.Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 5 pages a minute more than printer A ?

a. 600
b. 800
c. 1000
d. 1200
e. 1500

answer:
[Reveal] Spoiler:
A


2. A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 11:00 pm and not earlier, when was the drain opened?
a. at 2:00 pm
b. at 2:30 pm
c. at 3:00 pm
d. at 3:30 pm
e. at 4:00 pm

answer:
[Reveal] Spoiler:
D




3.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

answer:
[Reveal] Spoiler:
D
Senior Manager
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Re: Some Work problems: how to solve these algebraically? [#permalink] New post 23 May 2010, 23:09
TheGmatTutor wrote:
Hi all,

I have a couple questions regarding the work problems below. I know how to solve these through plugging in numbers or using the answer choices, but how would you solve these algebraically?

1.Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 5 pages a minute more than printer A ?

a. 600
b. 800
c. 1000
d. 1200
e. 1500

answer:
[Reveal] Spoiler:
A


2. A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 11:00 pm and not earlier, when was the drain opened?
a. at 2:00 pm
b. at 2:30 pm
c. at 3:00 pm
d. at 3:30 pm
e. at 4:00 pm

answer:
[Reveal] Spoiler:
D




3.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

answer:
[Reveal] Spoiler:
D


I think you should have posted all these questions in separate threads. Anyways, I will take a stab at the first question:

A + B --> 24 minutes
A = p / min
B = p + 5 / min
A + B will both produce pages in 24 minutes = 24p + 24(p+5) = 48p + 120
Total pages = 60p (As it takes A 60 minutes to finish the task)

Thus,
48p + 120 = 60p
p=10

Total pages = 10*60 = 600

Answer: A
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Joined: 15 Nov 2006
Posts: 326
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Re: Some Work problems: how to solve these algebraically? [#permalink] New post 23 May 2010, 23:17
For 2 :
Look at the Rates of filling and draining:
In 1 hr the pipe fills = 1/4 of the tank = 25%
In 1 hr the pipe drains = 1/5 = 20%
Thus if both are open the tank will be filled by = 5%

Using this I plugged in numbers for each choice and the only choice that stood out was C

C) At 3:30 the the filling pipe would hav filled 62.5% . The rest of 37.5% will be filled in 37.5/5= 7.5 hrs. This takes us to 11:00pm . Which is the answer

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Re: Some Work problems: how to solve these algebraically?   [#permalink] 23 May 2010, 23:17
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