Collection of work/rate problems?

How in the world am I going to solve that quadratic equation quickly in the actual exam? One of the answers is -1.20. I know a negative answer is not required but is there a faster way of doing this problem?

Thank you in advance.

You mean D: 3:30 right? Here is a different approach.

R = d/t
We know the the size of the pool (d) is the same.

So R1t1 = R2D2

or 1/4*10 = 1/5*t2
t2 = 50/4

Subtract this from 10: 10-50/4 = -2.5 (Ignore the negative)

Add this to 1 and gives you 3:30.

Does this method make sense?

8. Answer is 3:30 PM. The drain pipe has been opened at 3:30 pm..let me know if u need a solution

This question is solved wrongly. The correct answer is "B".

Statement 2 will be sufficient, since it gives us a comparison of X and Y's rates. We know: the amount of work Y did in 3 hours was half what X did in 4 hours. In other words, if X worked for 2 hours, X would do the same work that Y did in 3 hours. Since we know that 4 hours of X and 3 hours of Y is enough to finish the job, and 3 hours of Y is equivalent to 2 hours of X, then X working alone would take 6 hours to do the job.

11.6 machines each working at the same constant rate together can complete a job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

My Solution:

This Question is based on Mandays fundamental.

6 machines work for 12 days to complete 1 job= 6*12 mandays (machine=man)

Now if we reduce days in this formula, machines will increase to compensate the reduction in days :

so we have :

6 mac*12 days = x mac * 8 days
x= 9 machines - a delta of 3 machines in addition ANS = 3 machines

12.At their respective rates, pump A, B, and C can fulfill an empty tank, or pump-out the full tank in 2, 3, and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, in how many hours, the tank will be empty?
A. 2/3
B. 1
C. 3/4
D. 3/2
E. 2

My Approach - Supposedly the shortest and the best to solve such problems:

whenever we see such problems where time taken by pipes a (2), b(3) ,c(6) are given , take out the LCM of these values (the number which will be divisible of all these 3 values):
LCM of 2,3,6 = 12
Now this figure 12 is the total unit of Work (work done to fill full tank):
A does work -> 12/2= 6units /hour
B does work -> 12/3= 4units /hour
C does work -> 12/6= 2units /hour

for half tank -> total units of work=6 units
the equation can be written as -> x(-A-B+C) =6 (x is no of hours required and (-A-B+C) is work done in 1 hour - also '-' bcos A and B pumps out)

x(-6-4+2) = 6
x=-6/8 = 3/4

The explanation looks big, but if put inpractice, we can solve such questions without a pen-paper

Hi where can I get the full list of the answers. Am confused with different responses to same qs!

Can someone please explain to me how we solved to get D=4? I am having a tough time getting to this number. Thank you!

Check the solution here: work-problem-98599.html#p759876

Similar questions:
a-good-one-98479.html?hilit=point%20quadratic
hours-to-type-pages-102407.html?hilit=point%20quadratic

Hope it helps.
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Thanks Bunuel, this was very helpful! appreciate your responsiveness.

10.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?
* 12
* 18
* 20
* 24
* 30

Rate of printer A and printer B printing 40 pages together:

40 pages * 6 min / 50 pages

let B = # of mins for printer B to print 40 pages

Rate of Printer A + Rate of Printer B = Rate of Printer A and B
40/(B+4) + 40/B = 40*6/50
simplify:
-5B^2 + 28*B + 96 = 0
(I had to use the quadratic formula here)
B = 8

Rate of Printer A = 40 pages / (8+4) min

therefore

Rate of printer A to print 40 pages:

80 pages * (12 min / 40 pages) = 24 mins

ANSWER: D. 24 mins

This one took me a long time to solve... way more than 2 mins. If anyone finds a quicker way to solve this, please post!


There is a mistake in the explanation above.

The answer is indeed 24 mins, which is derived from the equation -5B^2 + 28*B + 96 = 0, just as h2polo said.

BUT->

Rate of Printer A + Rate of Printer B = Rate of Printer A and B = 40/(B+4) + 40/B = 40*6/50 ----- this is wrong; solve, and you get 24B^2 - 304*B - 800 = 0, which is not equal to -5B^2 + 28*B + 96 = 0.

Rate of Printer A and B = 40/(B+4) + 40/B = 50/6 ----- this is correct; from there you get -5B^2 + 28*B + 96 = 0, and then experience the enjoyment of finding its roots.

Positive root is 8 --> 8+4=12 is the time it takes A to print 40 pages --> 12*2=24 is the time it takes A to print 80 pages
Can somebody please break down this section:

Rate of Printer A and B = 40/(B+4) + 40/B = 50/6 ----- this is correct; from there you get -5B^2 + 28*B + 96 = 0

Im having difficulty doing the math...Much appreciated.

Thank you...

Casey

i am in the same boat as casey.....
Rate of Printer A and B = 40/(B+4) + 40/B = 50/6 ----- this is correct; from there you get -5B^2 + 28*B + 96 = 0

Im having difficulty doing the math...Much appreciated.
i know the 40/(B+4) + 40/B should be in the form XY/x+y...but i am not getting the final equation.

First of all: in case of any question or doubt about specific problem please post this problem in PS or DS subforum.

As for this problem:

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: \(2a=24\) --> \(a=12\) --> \(\frac{1}{12}+\frac{1}{8}=\frac{5}{24}\).

Answer: D.

Similar problems:
work-problem-98599.html#p759876
hours-to-type-pages-102407.html?hilit=answer%20choices%20or%20solve%20quadratic%20equation.%20R

Theory about work problems:
word-translations-rates-work-104208.html?hilit=printer#p812628

Hope it helps.
_________________

hi does anyone have the answers to 4, 5, 8, 9, 10, 11, 12, 17,18,19 ?

regards

I can't seem to figure out why you multiplied 1/3 by 7/5. I assume you are right because the answer I get isn't one of the choices, so I'm hoping someone can explain to me why this was done. I try to solve these problems using a small chart: (Total=Rate*Time)

As you stated, let's assume it takes 1 hr to make a B stereo.

Basic
Total = 2/3
Rate = x
time = 1hr
therefore rate (x) = (2/3) / 1 = 2/3

Deluxe
Total = 1/3
Rate = y
time = 7/5 *1hr = 7/5
therefore rate (y) = (1/3) / (7/5) = 5/21

so 1/x + 1/y = 1/total time (t)
1/(2/3) + 1/(5/21) = 1/t
t = 3/2 + 21/5 = 15/10 + 42/10 = 57/10

so to find the fraction of Deluxe Time/Total time = (7/5)/(57/10) = not the right answer

I can see that in order to match the snipertrader's solution, I need to rearrange my 'total', 'rate' & 'time' to be:

Basic
Total = x
rate = 1
time = 2/3

Deluxe
total = y
rate = 7/5
time = 1/3

in which case you would get 7/17 as the answer, but I can't make the leap as to why 2/3 and 1/3 need to be the TIME and not the TOTAL? I'm hoping someone can walk me through this.

Thank you!!

Answers to first 15.
1.40
2.C (8)
3.A(600)
4.8 1/3
6.2/3
7.C (97.2)
8.3:30pm
9.12,000
10. 24
11. 3
12. 3/4
13. D (1/8)
14. 10
15. C


Rest tomorrow.
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16. C x-3/3x
17. A 18
18. B 3
19. A 6
20. C 6
21. A 24
22 D 66 2/3
23.B 100
24 D 25
25 D 36
26 D 2/3
27.E 4/9
Missing Answer choices for Q.27 are: (A) 1/9 (B) 1/6 (C) 1/3 (D) 7/18 (E) 4/9
28. B
29. D 12/7
30. 7/17 A
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Need help understanding this
7.If Jim earns x dollars per hour, it will take him 4 hours to earn exactly enough money to purchase a particular jacket. If Tom earns y dollars per hour, it will take him exactly 5 hours to earn enough money to purchase the same jacket. How much does the jacket cost?
(1) Tom makes 20% less per hour than Jim does.
(2) x + y = $43.75

The answer is B, but I want to understand how I can figure this out without solving the whole problem.

From the question we have 4x = 5y

From (1) we have y = 0.8x (or y - 0.8x = 0)
From (2) we have x + y = 43.75 (or y = 43.75 - x)

At this point I see I have a new equation from both (1) and (2) and my initial response is that both are individually sufficient (D).

How can I figure out at this point that (1) is not sufficient and (2) is sufficient without spending much time in solving all the equations.

thanks,
Vinay

No need to use any algebra here.

A = tap that is filling the pool
B = leak in the pool

A is running for 10 hrs, which means it can fill 2.5 times the pool in that time.
However, it is able to fill just 1 pool, which means that B leaks 1.5 times the pool in that time. Now, B can empty 1 pool in 5 hrs, so it will take 7.5 hrs to empty 1.5 times the pool.

Therefore, leak started 2.5 hrs after A started = which is 3.30pm.