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Work Time problem.

by AndyB » Fri Nov 05, 2010 5:46 am
Hi All,

Could someone explain how should I approach the following problem.

Working together, A and B can complete an assigned task in 20 days. However, if A worked alone and complete half the work and then B takes over the task and completes the second half of the task, the task will be completed in 45 days. How long will A take to complete the task if he worked alone? Assume that B is more efficient than A.

A.25 days
B.30 days
C.60 days
D.65 days
E.36 days

Please help me I have just started my preparation.
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by kmittal82 » Fri Nov 05, 2010 8:58 am
In work-rate problems, you can add the rates (which is 1/time)

Let time taken by A to finish the job alone = a
Let time taken by B to finish the job alone = b

(1/a) + (1/b) = (1/20)

=> ab/(a+b) = 20

Time taken by A to finish half the work = a/2
Time taken by B to finish half the work = b/2

a/2 + b/2 = 45 => a + b = 90

Using this in the equation above, we get a*b = 1800 => b = 1800/a

Now use the answers to get a

(1) if a = 25, b = 72
(2) if a = 30, b = 60
(3) if a = 60, b = 30
(4) if a = 65, b = 1800/65
(5) a = 36, b = 50

Only options (3) and (4) show that B is more efficient tthan A, and given the nature of the answers, I would go for (C), since it is a whole number and not a fraction as (D)
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by GMATGuruNY » Fri Nov 05, 2010 9:06 am
AndyB wrote:Hi All,

Could someone explain how should I approach the following problem.

Working together, A and B can complete an assigned task in 20 days. However, if A worked alone and complete half the work and then B takes over the task and completes the second half of the task, the task will be completed in 45 days. How long will A take to complete the task if he worked alone? Assume that B is more efficient than A.

A.25 days
B.30 days
C.60 days
D.65 days
E.36 days

Please help me I have just started my preparation.
We could plug in the answer choices, which represent the time for A to complete the task alone. Since the task is undefined, we should plug in our own value for the task. To make the math easy, the value for the task should be divisible by 20 and 45 (the times given in the problem) and by the value in the answer choice.

Answer choice C: time for A alone = 60 days.
Let's plug in task = 180
Rate for A alone = w/t = 180/60 = 3/day.
Since A and B together can complete the task in 20 days, combined rate for A+B = w/t = 180/20 = 9/day.
Thus, rate for B alone = 9-3 = 6/day.
For A to complete half the task, t = w/r = 90/3 = 30 days.
Time for B to finish = w/r = 90/6 = 15 days.
Total time = 30+15 = 45 days. Success!

The correct answer is C.
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by MAAJ » Fri Nov 05, 2010 10:48 am
I got the answer (C)

Here's how I did it, but not 100% sure if its correct.

(1/a)+(1/b) = (1/20) [(1/a)= rate of A (1/b)= rate of B]

20(1/a) + 20 (1/b) = 1 [(20 days * rate A) + (20 days * rate B) = task]

Now they tells us that A makes the half of the task, and then B completes the other half at the time of 45 days, this is:

x (1/a) = 1/2 -> x/a = 1/2 -> 2x = a -> x = a/2
y (1/b) = 1/2 -> x/b = 1/2 -> 2x = b -> x = b/2
x + y = 45

Then I made the sustitution:

x + y = 45
(a/2) + (b/2) = 45
(a+b)/2 = 45
a+b = 90

Here I had to pick numbers that sumed would equal 90, but also could solve the first equation -> 20(1/a) + 20 (1/b) = 1. Also I had to asume that B is more efficient than A.

a-> 70 60 50
b-> 20 30 40

From these only a=60 and b=30 solve the equation. Lets look at it:

20(1/a) + 20 (1/b) = 1
20(1/60) + 20 (1/30) = 1
2/6 + 2/3 = 1 [Here we can see that B is more efficient than A because 2/3 > 2/6=1/3]
1/3 + 2/3 = 1
3/3=1
1=1

So now we know the rate of A and B, and now we have to find the time that A needs to complete the whole task.

z (1/a) = 1 [time * rate = task]
z (1/60) = 1
z/60 = 1
z = 60

It takes 60 days for the machine A to complete the task.
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by AndyB » Fri Nov 05, 2010 9:56 pm
Hi Maaz,

Thanks a lot for helping.
Your explanation help me figure out how a/2 +b/2 = 45.
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by AndyB » Fri Nov 05, 2010 10:03 pm
Hi Mitch,

Thanks a lot for the help.
Is there any trick in selecting "60" before trying other options...??
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by AndyB » Fri Nov 05, 2010 10:05 pm
Hi Kmittal,

Thanks for the help.
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by goyalsau » Sat Nov 06, 2010 1:04 am
GMATGuruNY wrote:
AndyB wrote:Hi All,

Could someone explain how should I approach the following problem.

Working together, A and B can complete an assigned task in 20 days. However, if A worked alone and complete half the work and then B takes over the task and completes the second half of the task, the task will be completed in 45 days. How long will A take to complete the task if he worked alone? Assume that B is more efficient than A.

A.25 days
B.30 days
C.60 days
D.65 days
E.36 days

Please help me I have just started my preparation.
We could plug in the answer choices, which represent the time for A to complete the task alone. Since the task is undefined, we should plug in our own value for the task. To make the math easy, the value for the task should be divisible by 20 and 45 (the times given in the problem) and by the value in the answer choice.

Answer choice C: time for A alone = 60 days.
Let's plug in task = 180
Rate for A alone = w/t = 180/60 = 3/day.
Since A and B together can complete the task in 20 days, combined rate for A+B = w/t = 180/20 = 9/day.
Thus, rate for B alone = 9-3 = 6/day.
For A to complete half the task, t = w/r = 90/3 = 30 days.
Time for B to finish = w/r = 90/6 = 15 days.
Total time = 30+15 = 45 days. Success!

The correct answer is C.

I tried it first by the equation method but failed , and then i tried it with options then i able to do it in time,
I was wondering what if this question comes in a DS form and then we were not given options, In that case I was not able to do it in time, for sure and not even correctly,
The technique the guys are suggested over here is good but i never able to do a Work Problem with out plugging numbers.

Can you please suggest some way by which work problems can be solved with simple equations and So that i can use it in future........ I don't know why Work equations are very tough for me or i am missing something...
Saurabh Goyal
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by GMATGuruNY » Sat Nov 06, 2010 3:13 am
AndyB wrote:Hi Mitch,

Thanks a lot for the help.
Is there any trick in selecting "60" before trying other options...??
Yes.

The problem states that A and B, working together, take 20 days to complete the task.
If A and B were working at the same rate, each would require double the amount of time to complete the task: 2*20 = 40 days.
Since the problem states that B is faster than A, B must take less than 40 days to complete the job alone, and A must take more than 40 days to complete the job alone.
Thus, the only answer choices that could be correct are C and D.
If C doesn't work, we can safely choose D as the correct answer. Either way, we need to try only one option.

Goyalsau asked about how to handle a DS question about rates. Remember the following:

If we know the combined time or rate for two people working together to complete a job, and we're given the time or rate for one of them, we can determine the time and rate for the other person. No need to set up equations.

If a DS question asks for a time or rate and we're not sure whether we have sufficient information, we can plug in two different values for the job. If the time or rate stays the same, we have sufficient information. If the time or rate changes, we have insufficient information.
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by goyalsau » Sat Nov 06, 2010 8:08 pm
GMATGuruNY wrote:
If a DS question asks for a time or rate and we're not sure whether we have sufficient information, we can plug in two different values for the job. If the time or rate stays the same, we have sufficient information. If the time or rate changes, we have insufficient information.


Dear Guru, thanks for the above explanation, I was able to figure out the above situation in a DS question,

But i am not to understand this one, Can you please explain it a with the help of a example so WE can understand it in a much better way,

Thanks Guru you are GREAT ( I have learned a lot from YOU , Especially the way you solve problem with options ) AWESOME
Saurabh Goyal
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by GMATGuruNY » Sun Nov 07, 2010 3:37 am
goyalsau wrote:
GMATGuruNY wrote:
If a DS question asks for a time or rate and we're not sure whether we have sufficient information, we can plug in two different values for the job. If the time or rate stays the same, we have sufficient information. If the time or rate changes, we have insufficient information.


Dear Guru, thanks for the above explanation, I was able to figure out the above situation in a DS question,

But i am not to understand this one, Can you please explain it a with the help of a example so WE can understand it in a much better way,

Thanks Guru you are GREAT ( I have learned a lot from YOU , Especially the way you solve problem with options ) AWESOME
Here's an example:

When Joan and Kyle work together, they can complete a job in 3 hours. If Joan works alone on the first half of the job and Kyle works alone on the remaining half of the job, how long will it take to complete the job?

1. Kyle could complete the whole job by himself in 4 hours.

To determine whether statement 1 is sufficient, we could plug in two different values for the job and see whether the time needed to complete the job stays the same (showing us that the statement is sufficient) or changes (showing us that the statement is insufficient).

Plug in job = 12.
Combined rate for J+K = w/t = 12/3 = 4.
Rate for K alone = w/t = 12/4 = 3.
Thus, rate for J alone = 4-3 = 1.
Time for J to complete half the job = w/r = 6/1 = 6.
Time for K to complete half the job = w/r = 6/3 = 2.
Total time = 6+2 = 8.

Plug in job = 24.
Combined rate for J+K = w/t = 24/3 = 8.
Rate for K alone = w/t = 24/4 = 6.
Thus, rate for J alone = 8-6 = 2.
Time for J to complete half the job = w/r = 12/2 = 6.
Time for K to complete half the job = w/r = 12/6 = 2.
Total time = 6+2 = 8.

Since the total time in both cases is 8 hours, the statement is sufficient.

Hope this helps!
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