It takes 4 cooks 4 hours to bake 4 cakes.

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ahmedshafea: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Wed Aug 30, 2017 10:04 am

It takes 4 cooks 4 hours to bake 4 cakes.

by ahmedshafea » Mon Sep 11, 2017 12:58 pm

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
14âˆ—4âˆ—414âˆ—4âˆ—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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Source: Beat The GMAT — Problem Solving | Mon Sep 11, 2017 12:58 pm

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by Brent@GMATPrepNow » Mon Sep 11, 2017 1:30 pm

ahmedshafea 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?

This tells us that EACH cook takes 4 hours to bake ONE cake
So, FOUR cooks take 4 hours to bake FOUR cakes (as in the question)
And,...EIGHT cooks take 4 hours to bake EIGHT cakes

Answer: 4 hours

Cheers,
Brent

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by [email protected] » Mon Sep 11, 2017 7:36 pm

Hi ahmedshafea,

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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by GMATGuruNY » Tue Sep 12, 2017 2:44 am

ahmedshafea 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
14âˆ—4âˆ—414âˆ—4âˆ—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.

Use the following equation:

(workers)(time) / output = (workers)(time) / output

In the equation above:
Workers and time are INVERSELY PROPORTIONAL.
As the number of workers increases, the amount of time required to produce the same output decreases.
Workers and output are DIRECTLY PROPORTIONAL.
As the number of workers increases, the amount of output also increases.
Time and output are also DIRECTLY PROPORTIONAL.
As the amount of time increases, the amount of output also increases.

In the problem above:
(4 cooks)(4 hours) / (4 cakes) = (8 cooks)(x hours) / (8 cakes)
4 = x.

The correct answer is 4 hours.

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by Scott@TargetTestPrep » Wed Jan 03, 2018 4:12 pm

ahmedshafea 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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