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

Question

01-01-2022
Mathematics

Answered

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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

Sagot :

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jimthompson5910 jimthompson5910 · Answer 1 · 2022-01-01T01:44:52-05:00

Answer: A) 3

=========================================================

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.

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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.

Sagot :

Answer: A) 3

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