Three machines, individually, can do a certain job in 4, 5,

Machine 1 in one hour can perform 1/4th job
Machine 2 in one hour can perform 1/5th job
Machine 3 in one hour can perform 1/6th job

Combinations of two machines working together can do 9/20, 10/24 and 11/30 parts of the job.

Now 9/20 is the greatest among the three combinations and hence B is the answer.

Whenever you see a work problem, jot down the formula W=RT (Work = Rate*Time).

We are looking for the greatest amount of work that can be done in 1 hour, so we look at the two machines with the two fastest rates.
Specifically the machines that finish the job in 4 and 5 hours whose rates are 1/4 and 1/5 respectively. (To find the rate given the time: If a machine finishes a task in 4 hours we think of the completed task as 1, so by plugging into the formula, we have W=RT, 1 = R*4 or 1/4 =Rate)

Since the machines are working together we add the individual rates together.
W = R*T
W = (1/4+1/5)*1
W = 9/20

B, here's why:

you can skip an awful lot of math if you recognize that the machines 1 and 2 are the fastest, so just combine their rates:

1 (job) / 4 (hrs) = 1/4 (job per hour)
1 (job) / 5 (hrs) = 1/5 (job per hour)

1/4 + 1/5 = 5/20 + 4/20 = 9/20 (jobs per hour)

--> every hour, Machines 1 and 2 together, can perform 9/20ths (or 45%) of the job, answer B

Note: no other combination (machine 1 and 3 together, or machine 2 and 3 together) can come close (since 3 is the slowest machine) so don't bother doing that math (@cssk: ur math was correct, but you did more work than you had to)

Three machines, individually, can do a certain job in 4, 5, and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?

(A) 11/30
(B) 9/20
(C) 3/5
(D) 11/15
(E) 5/6

Sol: We know Work= Rate*Time

The greatest part of the work in 1 hour will be done by machines which take the lowest time to get the work done individually. Here machines with individual rates and 4 and 5 hours will do the maximum work in 1 hour.

Work Done in 1 hour will be 1/4+1/5= 9/20.
Ans B

Three machines, individually, can do a certain job in 4, 5, and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?

(A) 11/30
(B) 9/20
(C) 3/5
(D) 11/15
(E) 5/6


Let us say that the total work is of 60 units then the number of units finished in one hour will be 15, 12 and 10 units per hour respectively.
Greatest number of units finished: 15 + 12 = 27

Fraction of work: 27/60 = 9/20

Assign a "nice" value to the job (i.e., a value that works well with the given numbers, 4, 5 and 6)
Since 4, 5 and 6 all divide into 60, let's say that completing the job means making 60 widgets

So, the first machine can make 60 in 4 hours, which means its rate is 15 widgets per hour.
The second machine can make 60 in 5 hours, which means its rate is 12 widgets per hour.
The 3rd machine can make 60 in 6 hours, which means its rate is 10 widgets per hour.

So, the first machine and second machine are the two fastest.
Their combined rate = 15 + 12 = 27 widgets per hour
So, in one hour, those two machines can make 27 widgets, which means they can complete 27/60 of the job.

27/60 simplifies to be 9/20
Answer: B

Solution:

We see that the rates of the three machines are 1/4, 1/5, and 1/6, respectively. Thus, if the two machines with the greatest rates work together, then the greatest part of the job that can be done in one hour is 1/4 + 1/5 = 5/20 + 4/20 = 9/20.

Answer: B

Solution :

Unit of work completed (LCM of time given for each machine, i,e 4,5 and 6) =60 Unit
No. of Unit by machine 1 = 60/4 = 15 unit
No. of Unit by machine 1 = 60/5 = 12 unit
No. of Unit by machine 1 = 60/10 = 6 unit

Greatest part of Job = 15+12 = 27 unit , 27/60 = 9/20

Let's consider all possible pairs of machines and find the rate at which they work together (in units per hour).

Machine A and B: A can do the job in 4 hours, so its rate is 1/4 of the job per hour. Similarly, B's rate is 1/5. Together, their rate is 1/4 + 1/5 = 9/20.

Machine A and C: A's rate is 1/4, and C's rate is 1/6. Together, their rate is 1/4 + 1/6 = 5/12.

Machine B and C: B's rate is 1/5, and C's rate is 1/6. Together, their rate is 1/5 + 1/6 = 11/30.

The question asks for the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates. So we want to find the maximum of the rates we just calculated.

The maximum is 9/20, which is achieved when machines A and B work together.

Therefore, the answer is (B) 9/20.

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