work problem - tutors help me please

[maoriba]

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

[GMATGuruNY]

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.

[diebeatsthegmat]

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?

[goyalsau]

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.