# 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(:

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• Kris S
Lv 4

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 Z
Lv 7

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.

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.