Homework Help: 10 men to build 120 houses in 60 hrs

Take your initial data and break it down to simpler information that you can then use to answer the given question. So in the first problem, it says it takes 10 men to build 120 houses in 60 hours. If 10 men can build 10*X houses, then one man can build 1*X houses in the same amount of time, right? So it takes 1 man 60 hours to build 12 houses. Now if it takes 12*Y hours to build to build 12 houses, then it takes Y hours to build 1 house, right? So it takes 1 man 5 hours to build 1 house.

Note that you could have broken it down the other way. If it takes 10 men 60 hrs to build 120 houses, then it takes 1 man 600 hours to build 120 houses, and so it takes him 600/120 = 5 hours to build 1 house.

Now start to answer the question (again, you can do this in two ways). If it takes 1 man 5 hours for 1 house, then it takes 1 man 5*60 = 300 hours for 60 houses, and thus it takes 5 men 300/5 = 60 hours for 60 houses. Going the other way, if it takes 1 man 5 hours for 1 house, then it takes 5 men 5/5 = 1 hour for one house, and so it takes 5 men 1*60 = 60 hours for 60 houses.

I think a general explanation might either have been too confusing, or would have just ended up giving you a formula that you could use to "plug and chug" your way through any of these problems, and if you are going to have such a formula you should figure it out yourself. But hopefully you've understood the reasoning in the above example and will be able to apply it generally.