SOLUTION: 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?

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Question 486302: 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?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
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:

%28W%5B1%5DT%5B1%5D%29%2FJ%5B1%5D+=+%28W%5B2%5DT%5B2%5D%29%2FJ%5B2%5D

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.

%283%2A14%29%2F1+=+%28W%5B2%5D6%29%2F1

42 = 6W2

 7 = W2

So it would take 7 snowplows, and since they have 3, they need 4 more.

Edwin