It takes 4 cooks 4 hours to bake 4 cakes.

This topic has expert replies
User avatar
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
14∗4∗414∗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.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

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
Brent Hanneson - Creator of GMATPrepNow.com
Image

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

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

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

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
14∗4∗414∗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.
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7223
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

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.

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage