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# if x men can build a house in y days. how many days will it take z men working at the same rate to build?

if x men can build a house in y days. how many days will it take z men working at the same rate to build the same house, expressed in terms of x, y, and z? show all work. thanks(:

### 4 Answers

- Kris SLv 41 decade agoFavorite Answer
Find the rate for one person in the group described in the first part of the sentence.

I'll put it in terms that are clearer:

If 2 men can build a house in 3 days, it would take 1 person 3*2=6 days. So it would take one person xy days.

The same job with 4 people would take 6/4=1 1/2 days

So it would take z men xy/z days.

- Rich ZLv 71 decade ago
It is (x/z) * y.

The x crew does it in y days so the issue is how does the group size z compare to the group x size. That ratio multiplied by the y days is how long it will take.

For example if the z crew is twice as big then the job will be done in half the time.

- ♪£yricảl♪Lv 41 decade ago
x men --> 1 house --> y days

1 man --> 1 house --> x *y = (xy) days

z men --> 1 house --> xy * z = xyz days

So, the answer is xyz days for z men to build the same house.