The LCM of 3 hours and 4 hours is 12 hours.
Since 4 persons can clean 1 house in 1 hour, then 3 times as many
persons, or 12 persons, can clean 1 house in 1/3 the time or 20
minutes. Therefore, 1/4 as many persons as 12, or 3 persons will
take 4 times as long as 12 will take, or 80 minutes, or 1 hour and
20 minutes.
Or if you prefer you can use the job-worker-time formula, which is:
where
W1 = the number of workers in the first situation.
T1 = the number of time units (hours 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 (hours in this case) in the second situation.
J2 = the number of jobs in the second situation.
W1 = 4 W2 = 3
T1 = 1 T2 = the unknown quantity
J1 = 1 J2 = 1
[There was only 1 house, so the number of jobs in both situations is 1.
4 = 3T2
Divide both sides by 3
= T2
= T2
Answer hours or 1 hour and 20 minutes.
Edwin
