Rate Problem

phoenix9801 wrote:Xavier and Yvette can complete a job in 1.2 hrs, and Xavier and Zed can complete that job in 1.5hrs. If Yvette and Zed can complete the same job in 2 hours, how many hours will it take all three people to complete that job if they work simultaneously at their respective constant rates and without a break?

A) 1
B) 2
C) 2:35
D) 3
E) It cannot be determined from the information given.

Let the job = 6 units.

Rate for X+Y = w/t = 6/(1.2) = 60/12 = 5 units per hour.
Rate for X+Z = w/t = 6/(1.5) = 60/15 = 4 units per hour.
Rate for Y+Z = w/t = 6/2 = 3 units per hour.

When elements work together, ADD THEIR RATES.
(X+Y) + (X+Z) + (Y+Z) = 5+4+3
2X + 2Y + 2Z = 12
X+Y+Z = 6 units per hour.

Thus, the time for X+Y+Z to complete the job = w/r = 6/6 = 1 hour.

The correct answer is A.

phoenix9801 wrote: In 9 days, a certain job can be completed by eight machines working simultaneously and at the same constant rate. How many fewer machines, each working at the same constant rate, would be needed to complete the job in 12 days?

A) 2
B) 3
C) 4
D) 6
E) 8

Approach 1:

Plug in a RATE FOR EACH MACHINE.

Let the rate for each machine = 1 unit per day.
Rate for 8 machines = 8 units per day.
Over 9 days, the number of units produced by 8 machines = r*t = 8*9 = 72 units.

For 72 units to be produced in 12 days, the number of units that must produced each day = 72/12 = 6 units per day.
Since 2 fewer units must be produced each day -- 6 units per day, down from 8 units per day -- 2 fewer machines are needed.

The correct answer is A.

Approach 2:

{number of machines)(number of days) = (number of machines)(number of days)

Thus:
(8 machines)(9 days) = (x machines)(12 days)
8 * 9 = x * 12
72 = 12x
x = 6.

Thus, for the job to be completed in 12 days, only 6 machines are needed -- 2 fewer machines.

GMATGuruNY wrote:

phoenix9801 wrote: In 9 days, a certain job can be completed by eight machines working simultaneously and at the same constant rate. How many fewer machines, each working at the same constant rate, would be needed to complete the job in 12 days?

A) 2
B) 3
C) 4
D) 6
E) 8

Approach 1:

Plug in a RATE FOR EACH MACHINE.

Let the rate for each machine = 1 unit per day.
Rate for 8 machines = 8 units per day.
Over 9 days, the number of units produced by 8 machines = r*t = 8*9 = 72 units.

For 72 units to be produced in 12 days, the number of units that must produced each day = 72/12 = 6 units per day.
Since 2 fewer units must be produced each day -- 6 units per day, down from 8 units per day -- 2 fewer machines are needed.

The correct answer is A.

Approach 2:

{number of machines)(number of days) = (number of machines)(number of days)

Thus:
(8 machines)(9 days) = (x machines)(12 days)
8 * 9 = x * 12
72 = 12x
x = 6.

Thus, for the job to be completed in 12 days, only 6 machines are needed -- 2 fewer machines.

Mitch shouldn't the answer for "How many fewer machines" should be 6 because the question is indirectly hinting that the machines are less than 8 and so the number of machines required for 12 days.

I mean should the answer be the difference in the number of machines or should it be the number required for 12 days? Please help..