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# Word Problems/Compound Proportion

Question
QUESTION: Hello:

Consider the following:
4 carpenters can build 8 houses in 10 days.
2 carpenters can build how many houses in 15 days?

Solution:
H = K*c*d, where K is some constant, at the moment unknown.

The problems provide information that will determine K.
In the specific problem, we know that

8 = K*4*10

So, K = 8/40 = 1/5.

We now can write
H = (1/5)*c*d

We were asked how many houses can two carpenters build in 15 days.

So, H = (1/5)*2*15 = 6.

My question is as follows: Can this calculation/solution be used to solve for the following?

4 carpenters can build eight houses in 10 days.
How many carpenters can build 6 houses in 15 days?

4 carpenters can build 8 houses in 10 days.
2 carpenters can build how many houses in 15 days?

Solution:
H = K*c*d, where K is some constant, at the moment unknown.

The problems provide information that will determine K.
In the specific problem, we know that

8 = K*4*10

So, K = 8/40 = 1/5.

We now can write
H = (1/5)*c*d

We were asked how many houses can two carpenters build in 15 days.

So, H = (1/5)*2*15 = 6.

My question is as follows: Can this calculation/solution be used to solve for the following?

4 carpenters can build eight houses in 10 days.
How many carpenters can build 6 houses in 15 days?

Yes, 8 = K * 4 * 10, so K = 8/40 = 1/5.
We can now get the equation for the 2nd question as 6 = (1/5)c(15).
Since 15/5 = 3, we have 6 = 3c.
Dividing by 3 gives us c = 2.

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

QUESTION: Hello:

I want to thank you for the reply.

How can I use this calculation to solve for the following?
I was not successful when I tried.

x = K*y*z, where K is some constant:

If 195 men working 10 hours a day can finish a job in 20 days, how many men must be employed to finish the job in 15 days if they work 13 hours a day?

Let y be the men and z be the hours per day.
The problem gives that when y = 195 and z = 10, x is 20 days.
This gives K by putting in the values.  Thus, 20 = K*195*10, so K = 2/195.

This is not really needed, though.
If it is to be done in 15 days rather than 20 days, that is 20/15 = 4/3 the number of men.
If the time worked per day is 13 hours instead of 8 hours, that is 8/13 the number of men.
Taking (4/3)(8/13) gives 32/39.

That gives 195*(32/39).  Since 195/39 = 5, that is 5*32 = 160.

Word Problems

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#### Scott A Wilson

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