Question 886201
<pre>

Two ways to work it.

First way:

The LCM of 1200 persons and 450 persons is 3600 persons.

3600 persons is 3 times as many persons as 1200 persons and
3600 persons is 8 times as many persons as 450 persons.

Since 450 persons can build 1 bridge in 45 days, then 

3600 persons can build 8 bridges in 45 days.

So only 1200 persons will take 3 times as long or 135 days to build 8 bridges.

So to build only 1 bridge it will take 1200 persons only 1/8th as long,
and
1/8th of 135 days is 135/8 = {{{16&7/8}}} days.

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Second way:

You can also use the worker-time-job formula, which is:

{{{(W[1]T[1])/J[1]}}}{{{""=""}}}{{{(W[2]T[2])/J[2]}}}

where

W<sub>1</sub> = the number of workers in the first situation.
T<sub>1</sub> = the number of time units (days in this case) in the first situation.
J<sub>1</sub> = the number of jobs in the first situation.

W<sub>2</sub> = the number of workers in the second situation.
T<sub>2</sub> = the number of time units (days in this case) in the second situation.
J<sub>2</sub> = the number of jobs in the second situation.

W<sub>1</sub> = 1200             W<sub>2</sub> = 450     
T<sub>1</sub> =  ? (unknown)     T<sub>2</sub> = 45
J<sub>1</sub> =  1               J<sub>2</sub> = 1

{{{(W[1]T[1])/J[1]}}}{{{""=""}}}{{{(W[2]T[2])/J[2]}}}

{{{(1200*T[1])/1}}}{{{""=""}}}{{{(450*45)/1}}}

{{{1200*T[1]}}}{{{""=""}}}{{{20250}}}

{{{T[1]}}}{{{""=""}}}{{{20250/1200}}}

Reduce that fraction by dividing numerator and
denominator by 150

{{{T[1]}}}{{{""=""}}}{{{135/8}}}

{{{T[1]}}}{{{""=""}}}{{{16&7/8}}} days

Edwin</pre>