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# Word Problems/Compound Proportion

Question
QUESTION: Hello:

How is the answer to this question determined?

Four carpenters can build eight houses in ten days. Two carpenters can build how may houses in 15 days?

ANSWER: 4 carpenters can build 8 houses in 10 days.

Since we are replacing 4 carpenters by 2 carpenters, we need to multiply by 2/4.
It can be seen the 2/4 is 1/2, and 8 house times 1/2 is 4 houses.

Since the problem has 10 days and the question has 15 days,
we than need to multiply by 15/10, which is the same as 3/2.
Thus, 4 * 3/2 = 6, so these 2 carpenters should be able to build 6 houses in 15 days.

---------- FOLLOW-UP ----------

QUESTION: Hello:

If I reduce the number of carpenters to 1 carpenter from 4 carpenters can build 8 houses in 10 days, I think I answer is 1 carpenter builds 2 houses in 1.5 days.

If I multiply 1 carpenter by 2, I get 2 carpenters.  If I multiply 2 houses by 2, I get 4 houses. So 2 carpenters build 4 houses in 1.5 days. (I think.)
If these two carpenters work for ten days, that is 10 days/1.5 days.  I do not know what to do next.

What do I need to think about to get the answer 6 houses?

If the 4 carpenters were split up into individuals over the 10 day period,
that would mean each one can build 2 houses in 10 days since 4 * 2 = 8.

We are given 4 carpenters can build 8 houses in 10 days.
That means a carpenter can build 2 houses in 10 days.

If the number of carpenters was reduced from 4 to only 1, that would manes only 1/4 of the labor would be done.  This would mean that it would take 1 carpenter 4 times as long.

If there are only 2 carpenters instead of 4, we would get 4/2 = 2,
If we needed to get the same amount done, it would require twice as long.

As was stated at the start, it takes 1 person a total of 40 hours to do the house.
If the number of employees is increased, divide 40 hours by the number of employees
that are there.

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thanks for the follow-up!

Word Problems

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#### Scott A Wilson

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