Question

Two machines in a car parts factory mold different parts that will eventually be put together in an assembly plant. the first machine makes a part every 12 seconds, and the second machine makes a part every 45 seconds. the quality control engineer tests these parts each time they both come out of the machines at the same time. how often does she test the parts? show your work and express your answer in minutes.

Answer 1

The quality control engineer tests the parts every 180 seconds, which is equal to 3 minutes.

Step-by-step explanation:

To determine how often the quality control engineer tests the parts, we need to find the least common multiple (LCM) of the two times it takes for the machines to produce a part. The first machine makes a part every 12 seconds, and the second machine makes a part every 45 seconds. To find the LCM, we list the multiples of each number and find the smallest number that appears in both lists:

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, ...

Multiples of 45: 45, 90, 135, 180, 225, 270, ...

The LCM of 12 and 45 is 180. Therefore, the quality control engineer tests the parts every 180 seconds, which is equal to 3 minutes.