Question

At a factory, Joe assembles 12 parts each minute. He

has assembled 156 parts when Sheila starts on the line,
assembling at a pace of 15 parts per minute. If their
assembly rates continue, will Sheila ever catch up to Joe?
Explain and show all work.

Answer 1

yes, after 52 minutes

Explanation:

If t represents the time in minutes each person is working after Sheila arrives, then the number of parts produced is ...

Eric: 156 +12t

Sheila: 15t

These values are equal when ...

156t +12t = 15t . . . . . Eric's part count is equal to Sheila's part count

156 = 3t . . . . subtract 12t

52 = t . . . . divide by 3

Sheila will catch up to Joe after 52 minutes.