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 = days.
------------------------------------------------------
Second way:
You can also use the worker-time-job formula, which is:
where
W1 = the number of workers in the first situation.
T1 = the number of time units (days in this case) in the first situation.
J1 = the number of jobs in the first situation.
W2 = the number of workers in the second situation.
T2 = the number of time units (days in this case) in the second situation.
J2 = the number of jobs in the second situation.
W1 = 1200 W2 = 450
T1 = ? (unknown) T2 = 45
J1 = 1 J2 = 1
Reduce that fraction by dividing numerator and
denominator by 150
days
Edwin
