BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

work problem - tutors help me please

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 10
Joined: Fri Apr 02, 2010 9:38 pm
Location: hong kong
Thanked: 2 times
GMAT Score:490

work problem - tutors help me please

by maoriba » Wed Nov 24, 2010 6:38 am
It takes n Type 1 machines six times as long to produce 120 bolts as it takes 2n Type 2 machines, with each machine running at a constant rate that is the same for all machines of a particular type. Together, one Type 1 machine and one Type 2 machine can make 24/n bolts in 4 hours. How many hours will it take for 5n Type 1 machines to produce 60 bolts?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 10

If type 1 and type 2 together make 24/n bottles in 4 hours, it means they make 24/4n in one hour, which is 6/n bottles.

so 6/n = type 1/h + type 2/h

At the same time if it takes "n Type 1 machines six times as long to produce 120 bolts as it takes 2n Type 2 machines", than
(speed type 1)/ (speed type 2)= (120/6x )/(120/x)= 120/6x * x/120 = 1/6, so

6*speed type 1= speed type 2.

6/n = 1/6 x + x

agh...i am massing it up, can anybody help, please?

thank u



So, if we are looking for how many hours will it take for 5n Type 1 machines to produce 60 bolts ,we first have to
riba made
Top
Source: — Problem Solving |
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 » Wed Nov 24, 2010 9:21 am
maoriba wrote:It takes n Type 1 machines six times as long to produce 120 bolts as it takes 2n Type 2 machines, with each machine running at a constant rate that is the same for all machines of a particular type. Together, one Type 1 machine and one Type 2 machine can make 24/n bolts in 4 hours. How many hours will it take for 5n Type 1 machines to produce 60 bolts?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
We can plug in a value for n and then plug in the answer choices. Let n=1. The question then becomes:

It takes 1 Type 1 machine six times as long to produce 120 bolts as it takes 2 Type 2 machines, with each machine running at a constant rate that is the same for all machines of a particular type. Together, one Type 1 machine and one Type 2 machine can make 24 bolts in 4 hours. How many hours will it take for 5 Type 1 machines to produce 60 bolts?

The combined rate for the 2 types of machines = 24 bolts/4 hours = 6 bolts per hour.
Now let's plug in the answer choices, which represent how long it will take 5 Type 1 machines to produce 60 bolts -- or, if we divide by 5, how long it will take 1 Type 1 machine to produce 60/5 = 12 bolts.

Answer choice C: 6 hours for each Type 1 machine to produce 12 bolts
Rate for each Type 1 machine = 12/6 = 2 bolts per hour.
Since the combined rate is 6 per hour and Type 1 produces 2 per hour, Type 2 produces 6-2 = 4 per hour.
Time for 1 Type 1 machine to produce 120 bolts = 120/2 = 60 hours.
Rate for 2 Type 2 machines = 2*4 = 8 per hour. Time to produce 120 bolts = 120/8 = 15 hours.
(Time for Type 1)/(Time for Type 2) = 60/15 = 4.
We need the Type 1 machine to take longer. Eliminate A, B and C.

Answer choice D: 8 hours for each Type 1 machine to produce 12 bolts
Rate for each Type 1 machine = 12/8 = 1.5 bolts per hour.
Since the combined rate is 6 per hour and Type 1 produces 1.5 per hour, Type 2 produces 6-(1.5) = 4.5 per hour.
Time for 1 Type 1 machine to produce 120 bolts = 120/(1.5) = 80 hours.
Rate for 2 Type 2 machines = 2*(4.5) = 9 per hour. Time to produce 120 bolts = 120/9 = 40/3 hours.
(Time for Type 1)/(Time for Type 2) = 80/(40/3) = 6. Success!

The correct answer is D.
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
Top
Legendary Member
Posts: 1119
Joined: Fri May 07, 2010 8:50 am
Thanked: 29 times
Followed by:3 members

by diebeatsthegmat » Wed Nov 24, 2010 7:32 pm
GMATGuruNY wrote:
maoriba wrote:It takes n Type 1 machines six times as long to produce 120 bolts as it takes 2n Type 2 machines, with each machine running at a constant rate that is the same for all machines of a particular type. Together, one Type 1 machine and one Type 2 machine can make 24/n bolts in 4 hours. How many hours will it take for 5n Type 1 machines to produce 60 bolts?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
We can plug in a value for n and then plug in the answer choices. Let n=1. The question then becomes:

It takes 1 Type 1 machine six times as long to produce 120 bolts as it takes 2 Type 2 machines, with each machine running at a constant rate that is the same for all machines of a particular type. Together, one Type 1 machine and one Type 2 machine can make 24 bolts in 4 hours. How many hours will it take for 5 Type 1 machines to produce 60 bolts?

The combined rate for the 2 types of machines = 24 bolts/4 hours = 6 bolts per hour.
Now let's plug in the answer choices, which represent how long it will take 5 Type 1 machines to produce 60 bolts -- or, if we divide by 5, how long it will take 1 Type 1 machine to produce 60/5 = 12 bolts.

Answer choice C: 6 hours for each Type 1 machine to produce 12 bolts
Rate for each Type 1 machine = 12/6 = 2 bolts per hour.
Since the combined rate is 6 per hour and Type 1 produces 2 per hour, Type 2 produces 6-2 = 4 per hour.
Time for 1 Type 1 machine to produce 120 bolts = 120/2 = 60 hours.
Rate for 2 Type 2 machines = 2*4 = 8 per hour. Time to produce 120 bolts = 120/8 = 15 hours.
(Time for Type 1)/(Time for Type 2) = 60/15 = 4.
We need the Type 1 machine to take longer. Eliminate A, B and C.

Answer choice D: 8 hours for each Type 1 machine to produce 12 bolts
Rate for each Type 1 machine = 12/8 = 1.5 bolts per hour.
Since the combined rate is 6 per hour and Type 1 produces 1.5 per hour, Type 2 produces 6-(1.5) = 4.5 per hour.
Time for 1 Type 1 machine to produce 120 bolts = 120/(1.5) = 80 hours.
Rate for 2 Type 2 machines = 2*(4.5) = 9 per hour. Time to produce 120 bolts = 120/9 = 40/3 hours.
(Time for Type 1)/(Time for Type 2) = 80/(40/3) = 6. Success!

The correct answer is D.
thanks for nice explanation, however may you please explan the solution by a different way which dont use the answers?
Top
User avatar
Legendary Member
Posts: 866
Joined: Mon Aug 02, 2010 6:46 pm
Location: Gwalior, India
Thanked: 31 times

by goyalsau » Wed Nov 24, 2010 11:24 pm
GMATGuruNY wrote: We can plug in a value for n and then plug in the answer choices. Let n=1. The question then becomes:

It takes 1 Type 1 machine six times as long to produce 120 bolts as it takes 2 Type 2 machines, with each machine running at a constant rate that is the same for all machines of a particular type. Together, one Type 1 machine and one Type 2 machine can make 24 bolts in 4 hours. How many hours will it take for 5 Type 1 machines to produce 60 bolts?
.
I think the most important part of this problem to consider the value of n = 1

Lets assume that type 1 machine do x work in one hour,
So two type 2 machines must do 6x work in one hour, Because two (2) type 2 machines takes 1/6 of the time do the same work

So one machine of type 2 must do 6x/2 = 3x of the work in one hour,

Together they do 24x work in 4 hours,

In One hour they do 6x work Together,

x + 3x = 6x
x = 1.5

It means type one machine do 1.5 work in one hour and type two machine does 4.5 work in one hour.

Together they do 6 work in one hour , so 24 work in 4 hours,

so 5 type one machines will do 7.5 work in one hour

60/ 7.5 = 8 hours.
Saurabh Goyal
[email protected]
-------------------------


EveryBody Wants to Win But Nobody wants to prepare for Win.
Top
Post new topic Post Reply
• Page 1 of 1