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It takes 4 cooks 4 hours to bake 4 cakes.

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It takes 4 cooks 4 hours to bake 4 cakes.  [#permalink]

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New post 11 Sep 2017, 03:53
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It takes 4 cooks 4 hours to bake 4 cakes. Assuming no change of rate, how many hours will it take 8 cooks to bake 8 cakes?

I really can't solve this problem. I am having problem in approach.
Every time I see work problems I am stuck in approach.

In this question, I was approaching like
\(\frac{1}{4*4*4}\)

calculating the cakes baked by 1 cook in 1 hour. I don't even know if I am right.
but now I am stuck can anyone help me.
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It takes 4 cooks 4 hours to bake 4 cakes.  [#permalink]

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New post 11 Sep 2017, 09:25
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vishuboy wrote:
It takes 4 cooks 4 hours to bake 4 cakes. Assumingno change of rate, how many hours will it take 8 cooks to bake 8 cakes?

I really can't solve this problem. I am having problem in approach.
Every time I see work problems I am stuck in approach.

In this question, I was approaching like
\(\frac{1}{4*4*4}\)

calculating the cakes baked by 1 cook in 1 hour. I don't even know if I am right.
but now I am stuck can anyone help me.

Attachment:
WRTvariation.png
WRTvariation.png [ 17.23 KiB | Viewed 2907 times ]

The resources Bunuel listed are very helpful.

I don't know exactly where you are lost. (No, you are not correct about individual rate, but you are very close!)

There is one basic approach that might help.

Use the standard RT=W formula, but add "number of workers" (or machines, etc.) to the left hand side of that formula.

See the table above. It is a standard RTW table, but one column has been added: # of workers.

We can manipulate RT=W. We can manipulate, exactly the same way, #*R*T = W

First we need individual rate at which the bakers work, i.e. how many cakes per hour does an individual baker make?

We get that rate from the first scenario. Then we use that rate to solve the second scenario.

1. Find individual rate from first scenario

Manipulate the equation from above (# of workers) * r * t = W
# of workers = 4
Rate = ??
Time = 4
Work = 4

Plugging into the formula: 4 * Rate * 4 = 4
Rate = \(\frac{4}{(4 * 4)}\) = \(\frac{1}{4}\)

(The rate is in cakes/hour. )

2. Use that individual baker rate, and manipulate the equation again for the second scenario. This time you need to find time.

Basic equation once more is (# of workers) * r * t = W
rate of individual worker =\(\frac{1}{4}\)
# of workers = 8
Work = 8

Plugging into equation:

\(8 * \frac{1}{4} * time = 8\)

\((\frac{8}{4})(Time) = 8\)

\(2*(Time) = 8\)

Time = 4 hours

Hope that helps.
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Re: It takes 4 cooks 4 hours to bake 4 cakes.  [#permalink]

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New post 11 Sep 2017, 07:01
1
1
vishuboy wrote:
It takes 4 cooks 4 hours to bake 4 cakes. Assuming no change of rate, how many hours will it take 8 cooks to bake 8 cakes?

I really can't solve this problem. I am having problem in approach.
Every time I see work problems I am stuck in approach.

In this question, I was approaching like
\(\frac{1}{4*4*4}\)

calculating the cakes baked by 1 cook in 1 hour. I don't even know if I am right.
but now I am stuck can anyone help me.


4 cooks take 4 hours to bake 4 cakes;
4*2 = 8 cooks will take 4/2 = 2 hours to bake 4 cakes;
8 cooks will take 2*2 = 4 hours to bake 4*2 = 8 cakes.

Or simply twice as many cooks will make twice as many cakes in the same amount of time.

17. Work/Rate Problems



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Re: It takes 4 cooks 4 hours to bake 4 cakes.  [#permalink]

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New post 11 Sep 2017, 11:06
1
genxer123 wrote:
vishuboy wrote:
It takes 4 cooks 4 hours to bake 4 cakes. Assumingno change of rate, how many hours will it take 8 cooks to bake 8 cakes?

I really can't solve this problem. I am having problem in approach.
Every time I see work problems I am stuck in approach.

In this question, I was approaching like
\(\frac{1}{4*4*4}\)

calculating the cakes baked by 1 cook in 1 hour. I don't even know if I am right.
but now I am stuck can anyone help me.

Attachment:
WRTvariation.png

The resources Bunuel listed are very helpful.

I don't know exactly where you are lost. (No, you are not correct about individual rate, but you are very close!)

There is one basic approach that might help.

Use the standard RT=W formula, but add "number of workers" (or machines, etc.) to the left hand side of that formula.

See the table above. It is a standard RTW table, but one column has been added: # of workers.

We can manipulate RT=W. We can manipulate, exactly the same way, #*R*T = W

First we need individual rate at which the bakers work, i.e. how many cakes per hour does an individual baker make?

We get that rate from the first scenario. Then we use that rate to solve the second scenario.

1. Find individual rate from first scenario

Manipulate the equation from above (# of workers) * r * t = W
# of workers = 4
Rate = ??
Time = 4
Work = 4

Plugging into the formula: 4 * Rate * 4 = 4
Rate = \(\frac{4}{(4 * 4)}\) = \(\frac{1}{4}\)

(The rate is in cakes/hour. )

2. Use that individual baker rate, and manipulate the equation again for the second scenario. This time you need to find time.

Basic equation once more is (# of workers) * r * t = W
rate of individual worker =\(\frac{1}{4}\)
# of workers = 8
Work = 8

Plugging into equation:

\(8 * \frac{1}{4} * time = 8\)

\((\frac{8}{4})(Time) = 8\)

\(2*(Time) = 8\)

Time = 4 hours

Hope that helps.




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Re: It takes 4 cooks 4 hours to bake 4 cakes.  [#permalink]

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New post 11 Sep 2017, 11:14
It takes 16 man-hours(4 cooks x 4 hours) for 4 cakes
So, it takes 16/4 man-hours for 1 cake

Now to make 8 cakes, we would need 8x4=32 man-hours
We already have 8 cooks with us, and so the number of hours these 8 cooks would need is 32/8=4 hours

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Re: It takes 4 cooks 4 hours to bake 4 cakes.  [#permalink]

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New post 14 Sep 2017, 09:35
vishuboy wrote:
It takes 4 cooks 4 hours to bake 4 cakes. Assuming no change of rate, how many hours will it take 8 cooks to bake 8 cakes?


The rate of 4 cooks is 1 cake per hour. We can use a proportion to determine the rate of 8 cooks.

1/4 = x/8

x = 2

Since rate of 8 cooks is 2 cakes per hour, it will take 8/2 = 4 hours to bake 8 cakes.
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Re: It takes 4 cooks 4 hours to bake 4 cakes.  [#permalink]

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New post 06 Oct 2017, 11:00
The time will remain the same.
time taken by one cook to bake one cake is 4 hours
4 cooks to bake 4 cakes = 4 hours
8 cooks to bake 8 cakes = 4 hours

as the rate of a single cook is one cake in 4 hours.
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Re: It takes 4 cooks 4 hours to bake 4 cakes.  [#permalink]

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New post 09 Nov 2017, 20:33
Unitary method will never fail you in these cases.

4 cooks - 4 cakes - 4 hours
1 cook - 1 cake -4 hours

At this point you can say, using logic, that 8 cooks will bake 8 cakes in 4 hours.

If it is not clear, continue to find:
1 cook bakes \(\frac{1}{4}\) of a cake - 1 hour. (this is the individual rate of one cook. In most cases you will benefit by finding the individual rate but not always)

For 8 cooks, the rate is \(8*\frac{1}{4}\) = 2

Now W=8 ; R = 2 and T =?
W=RT
T = 4 hours.
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Re: It takes 4 cooks 4 hours to bake 4 cakes.  [#permalink]

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New post 07 Dec 2017, 13:31
1
Hi All,

When dealing with these types of rate questions, it helps to define the amount of 'work' needed to get to the end result.

Here, we're told that there are 4 cooks working 4 hours each... this means that there are
(4 cooks)(4 hours each) = 16 hours of cook-time needed to make those 4 cakes.

By extension, each cake takes 16/4 = 4 hours of cook-time. Thus, to make 1 cake, you could have...
1 cook work for 4 hours
2 cooks work for 2 hours each
4 cooks work for 1 hour each
8 cooks work for 1/2 hour each.
Etc.

We're asked how long it would take 8 cooks to make 8 cakes... Since each cake requires 4 hours of cook-time, it would take (8)(4) = 32 hours of cook-time to make those 8 cakes. With 8 cooks, that would be 32/8 = 4 hours each.

Final Answer:
4 hours


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Re: It takes 4 cooks 4 hours to bake 4 cakes. &nbs [#permalink] 07 Dec 2017, 13:31
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