Problem Solving

Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?"

A) 2
B) 3
C) 4
D) 6
E) 7

1) 6 machines complete a job in 12 days.
translates to 6 machines do 1/12 job in 1 day.

2) so 1 machine is 1/6M does 1/12J in 1 day.

using rate * distance = time

1/6M * 1/12J = 1/72MJ

3) To translate how many machines are required in 8 days:
each machine would have to 1/8J

such that 1/72 MJ / 1/8J = 1/9M 9 machines are required

9 - 6 = 3 additional machines

A helpful technique for work problems:

When the job is undefined, try plugging in your own number for the job.

Say each machine produces one unit per day. Then the 6 machines would produce 6 units each day. Over 12 days, 6 * 12 = 72 units would be produced.

If we want to produce the 72 units in only 8 days, we'll need 72 / 8 = 9 units to be produced each day.

Since we'll need 3 more units per day to be produced, and each machine produces 1 unit per day, we'll need 3 more machines.

The correct answer is B.