It takes 20 men 60 days to complete a building work. how many days longer would
it take 15 men, assuming that they all work at the same rate (formula method)
You want the formula method but first, this is the best way:
Get the least common multiple of two of the corresponding given quantities.
Think of what would happen if you had that least common multiple instead.
Then think of what would happen if you had the other quantity.
The least common multiple of 20 men and 15 men is 60 men.
Since it takes 20 men 60 days to complete a building work,
three times as many men, 60, will take 1/3 as long, or 20 days.
Then, one fourth as many men as that, 15, will take 4 times as long or 80 days.
Then 80 days is 20 more days than 60.
But your prof doesn't like reasoning it out, and wants you to plug in a formula.
OK, let's humor your prof.
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 done 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 done in the second situation.
W1 = 20 W2 = 15
T1 = 60 T2 = unknown quantity
J1 = 1 J2 = 1
80 days is 20 more days than 60. Answer: 20 days.
Edwin