It takes 3 city snowplows 14 hours to clear 500 miles of road. If the city wants the 500 miles of road to be cleared in 6 hours, how many additional snowplows must they buy?
The least common multiple of 14 hours and 6 hours is 42 hours.
It takes 3 city snowplows 14 hours
It takes 1 city snowplow 3 times as long or 42 hours
6 hours is 1/7th as long as that.
The city wants it done 7 times as fast as one snowplow can do it.
So it need 7 snowplows. It now has 3, so it needs 4 additional snowplows.
Or you can use the formula:
where
W1 = the number of workers (or machines) in the first situation.
T1 = the number of time units (hous, days, etc) in the first situation.
J1 = the number of jobs to be done in the first situation.
W2 = the number of workers (or machines) in the second situation.
T2 = the number of time units (hous, days, etc) in the second situation.
J2 = the number of jobs to be done in the second situation.
In this problem
W1 = 3, T1 = 14, J1 = 1,
W2 = ???, T2 = 6, J2 = 1.
42 = 6W2
7 = W2
So it would take 7 snowplows, and since they have 3, they need 4 more.
Edwin