Two Rate problems - Machines and Pumps

[zatar]

Disclaimer - these OG problems are from a practice cat, so if you haven't taken an official practice, please ignore these problems so that you dont artificially inflate your score.

1) Pumps A, B, and C, operate at respective rates. Pumps A & B fill a tank in 6/5 hours, A&C in 3/2 hours, pumps B&C in 2 hours, how long would A B and C take to fill the tank?

- 2
- 3
- 4
- 6
- 8

2) Six Machines each working at a constant rate can complete a job in 12 days, how many additional machines would be needed to complete the job in 8 days?

- 1/3
- 1/2
- 2/3
- 5/6
- 1

I am more interested in the processing of beating the questions, not the final answer. Your help will be greatly appreciated - thanks!

[GMATGuruNY]

For the first problem, the answer choices should read as follows:

Pumps A, B and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B and C, operating simultaneously, to fill the tank?

A)1/3
B)1/2
C)2/3
D)5/6
E)1

Let the pool = 18 units.

Rate for A+B = w/t = 18/(6/5) = 15 units per hour.
Rate for A+C = w/t = 18/(3/2) = 12 units per hour.
Rate for B+C = w/t = 18/2 = 9 units per hour.

Combining the rates:
(A+B) + (A+C) + (B+C) = 15+12+9 = 36.
2A + 2B + 2C = 36.
A+B+C = 18 units per hour.

Time for A+B+C to fill the pool = w/r = 18/18 = 1 hour.

The correct answer is E.

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Hi Zatar,

It appears that you've "flip-flopped" the answer choices for the two questions (meaning that the answers for the first question actually belong on the second question, and vice-verse).

For the second question, here' s one way to approach it.

Since 6 machines are working for 12 days, they will create 6(12) = 72 machine-days of work to complete a job.

The means that 1 machine, working for 1 day, will do 1/72 of the job.

The question asks about doing the work in 8 days, which means that we'll need X(8) = 72 machines. X = 9. The question asks how many ADDITIONAL machines are needed to go along with the 6 machines that we already have, so the answer is 3.

GMAT assassins aren't born, they're made,
Rich

[theCodeToGMAT]

2) Six Machines each working at a constant rate can complete a job in 12 days, how many additional machines would be needed to complete the job in 8 days?

- 1/3
- 1/2
- 2/3
- 5/6
- 1

Question 2:

W = R x T

R = 6

T = 12 days

Workdone = 72

FOr Additional Machines,

Rate = x

T = 8 days

W = 72

72 = x(8) => x = 9

Additional Machines = 9-6 = 3

[theCodeToGMAT]

1) Pumps A, B, and C, operate at respective rates. Pumps A & B fill a tank in 6/5 hours, A&C in 3/2 hours, pumps B&C in 2 hours, how long would A B and C take to fill the tank?

- 1/3
- 1/2
- 2/3
- 5/6
- 1

1/A + 1/B = 5/6
1/A + 1/C = 2/3
1/B + 1/C = 1/2

To find: 1/(1/A + 1/B + 1/C)

Add all three equations

2(1/A + 1/B + 1/C ) = (5+4+3)/6

1/A + 1/B + 1/C = 12/12 = 1

[Mathsbuddy]

1) Pumps A, B, and C, operate at respective rates. Pumps A & B fill a tank in 6/5 hours, A&C in 3/2 hours, pumps B&C in 2 hours, how long would A B and C take to fill the tank?

- 1/3
- 1/2
- 2/3
- 5/6
- 1

1/A + 1/B = 5/6
1/A + 1/C = 2/3
1/B + 1/C = 1/2

To find: 1/(1/A + 1/B + 1/C)

Add all three equations

2(1/A + 1/B + 1/C ) = (5+4+3)/6

1/A + 1/B + 1/C = 12/12 = 1

Nice! Exactly as I did it.