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?
<pre>
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:

{{{(W[1]T[1])/J[1] = (W[2]T[2])/J[2]}}}

where 

W<sub>1</sub> = the number of workers (or machines) in the first situation.
T<sub>1</sub> = the number of time units (hous, days, etc) in the first situation.
J<sub>1</sub> = the number of jobs to be done in the first situation.

W<sub>2</sub> = the number of workers (or machines) in the second situation.
T<sub>2</sub> = the number of time units (hous, days, etc) in the second situation.
J<sub>2</sub> = the number of jobs to be done in the second situation.

In this problem

W<sub>1</sub> = 3, T<sub>1</sub> = 14, J<sub>1</sub> = 1,
W<sub>2</sub> = ???, T<sub>2</sub> = 6, J<sub>2</sub> = 1.

{{{(3*14)/1 = (W[2]6)/1}}}

42 = 6W<sub>2</sub>

 7 = W<sub>2</sub>

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

Edwin</pre>