It takes A 12 days to make a batch of machine parts alone and B 18
days to make them alone. After 6
days of cooperation, A has some
other things to do and left the
rest to be done by B. How many
more days will it take B to
complete the work?
PLEASE EXPLAIN HOW TO SOLVE THIS MY TEACHER WANTS THE WORK
A. 3
B. 5
C. 2
D. 7

Explanation:

Let's say there are 216 machine parts that need to be made. I'm using this number since 12*18 = 216. Refer to the note at the bottom.

If person A works alone, then they can make those 216 parts in 12 days. Person A's unit rate is 216/12 = 18 parts per day.

Person B, working alone, has a rate of 216/18 = 12 parts per day.

If they work together without hindering one another, then their combined unit rate is 18+12 = 30 parts per day.

Working together for 6 days leads to 6*30 = 180 parts made so far. That leaves 216 - 180 = 36 parts left over for person B to finish up.

Since person B does so at a unit rate of 12 parts per day, this means person B needs 36/12 = 3 extra days.

Side note: There's nothing special about the value 216 I picked. I only selected that value so that dividing over 12 and 18 led to whole number results. You could pick the LCM of 12 and 18 to get the same idea.