5 identical snow plows can clear an iced parking lot in 12 hours. How long would it take 6 such snow plows to clear the same parking lot?
A. 1 hour, 15 minutes B. 2 hours, 30 minutes C. 3 hours D. 7 hours, 30 minutes E. 10 hours
(E) For a problem where a job size remains the same, but the number of workers changes, there is a very intuitive way to get to the answer, without using algebra. For example, if we double the number of workers on a job, it should take half the time. If we triple the number of workers on a job, it should take one-third the time. Similarly, if we use one-half the number of workers on a job, it should take twice the time. There is a nice reciprocal relationship here, so even when the numbers are not as easy to deal with, the relationship still holds.
So, in increasing the number of plows from 5 to 6, we are using 6/5 as many plows. So clearing the lot should take 5/6 the time: (5/6)(12) = 10 = 10 hours. The correct answer is choice (E). -------------
For 5 snow plows to take 12 hours, would each take 5/12 or 2.4 hours and then you combine them?
1) The common approach for this type of the questions is to calculate the rate of a unit. In other words "how much of the parking lot does a snow plow clear in 1 hour"? We start with the fact that 5 snow plows clear the parking lot in 12 hours. On the diagram we show a rectangular parking lot, but the shape of the parking does NOT affect the reasoning.
2) Since 5 snow plows clear the iced parking lot in 12 hours, then each of the snow plows clears 1/5 of the parking lot.
3) Since a snow plow clears 1/5 of the parking lot in 12 hours, then in 1 hour it clears (1/5)/12 of the parking lot. (1/5)/12 = 1/(5 × 12) = 1/60 Now we have a rate for one snow plow. That's the key moment to all such questions.
4) Since a snow plow clears 1/(5 × 12) of the parking lot in 1 hour, then 6 snow plows clear 6 × 1/(5 × 12) = 1/10 of the parking lot in 1 hour.
5) Since 6 snow plows clear 1/10 of the parking lot in 1 hour, then to clean the whole parking lot it will take them 1 / (1/10) = 10 hours. The correct answer is A.
----------- This is the basic logic that stands behind all of questions of this type. Once you understand it, you can take shortcuts, like using the whole formula at once:
new time = 1 / ([the rate of 1] × 6) new time = 1 / (1 / (5 × 12) × 6) = 1 / 0.1 = 10
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