Six men can build a house in 3 days. Assumming that all of the workmen work at the same rate. How many workmen would it take to build the house in one day?

Question

Show your reasoning as well. Thank you!

Answer 1

The first step is to translate the word problem into equations we can work with.

 

We know the following:

 

1. Six men can build a house in 3 days.

2. All six men work at the same rate.

 

Let M = the rate of work of a single man (in houses per day)

Let H = a house,

Therefore:

 

6 * M  * 3 days = H

 

If we multiply this out, we get the following:

 

18 * M * 1 day = H

 

Therefore, it will take 18 men 1 day to build a single house.

Answer 2

The number of men (work) is inversely related to the days (time).

If the work is to be done in 1/3 the time, then 3 times as many workers are needed.

Eighteen men can complete the house in one day.