5 identical snow plows can clear an iced parking lot in 12 h

Question

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 hourss

Bunuel · Answer

6/5 as many plows will take 5/6 as many hours --> 12*5/6=10 hours.

Answer: E.

Manofsteel · Answer

x - rate of work done by 1 plow in 1 hour

Since all plows are identical:-
Total work done by 5 plows in 12hrs = 5*x*12
Total work done by 6 plows in 'y'hrs = 6*x*y

Since both the work done is same equate both:-
5*x*12 = 6*x*y

solving the above we get y = 10hrs

Answer (E)

sanjoo · Answer

i tuk the rate ..5/12.. and multiplied it with 6..got 2.5 hours..or 2 hours 30 mints

how to know, which approach we shud use..

Bunuel · Answer

The rate is (job)/(time). Why is 5/12 the rate?..

5*(the rate of 1 plow)*12 = (1 job);
6*(the rate of 1 plow)*x = (1 job);

5*(the rate of 1 plow)*12 = (1 job) = 6*(the rate of 1 plow)*x

5*12 = 6x --> x = 10 hours.

Hope it helps.

Nadiuska · Answer

I'm confused with this question. My understanding is wrong, but I don't know why is wrong. I don't know if the problem is because I'm assuming they're working together, but as I understand it is: 5/12 then 6/x x= 14.4. Which doesn't make sense. Can anyone help providing any further explanation?

Thanks!

Thanks!

Nadiuska · Answer

I'm confused with this question. My understanding is wrong, but I don't know why is wrong. I don't know if the problem is because I'm assuming they're working together, but as I understand it is: 5/12 then 6/x x= 14.4. Which doesn't make sense. Can anyone help providing any further explanation?

Thanks!

Thanks!

Bunuel · Answer

Can you please show why are you equating 5/12 and 6/x? What exactly are 5/12 and 6/x? Have you read this: 5-identical-snow-plows-can-clear-an-iced-parking-lot-in-12-h-167835.html#p1335684

eegalindo · Answer

I did this a little differently.

We know that  5r_1=12 , where  r_1  equals the hours each machine takes to clean their respective section of the lot.
Solving for  r_1  yields  r_1=2.4

Using the same approach for 6 machines yields:
 6r_2=12 
 =>r_2=2

I then did a percent change:
 \frac{2.4-2}{2.4}\approx{0.17}

That is we can expect a 17% change in our total time. Which yields,
 12*0.17  \approx{2} .

Thus,  12-2=10 . The answer is E.

This may not prove to be the most time efficient way, but I sometimes find it helpful in rate/work problems to think of % change to help visualize what the problem is asking. I also find that it's not too hard to estimate these numbers to get a more educated guess. When I initially did this problem I actually came up with a 20% change because I rounded to make the math easier. When using 20%, you get an answer of 9.6 hours total which for me was enough to know the answer was E.

EMPOWERgmatRichC · Answer

Hi eegalindo,

Unfortunately, you've interpreted this prompt incorrectly and your solution includes an equation that is NOT correct (we have no idea what 6r2 actually equals, so you cannot set it equal to 12). However, you were still able to get to the correct answer since the answer choices were so 'spread out.'

To start, in these types of prompts, the entities (in this case, the snow plows) are EACH working for the ENTIRE length of time. So the 5 machines EACH work for 12 hours, which creates (5)(12) = 60 machine-hours of work needed to complete the task. Knowing that 'requirement', you can now calculate how long it would take ANY number of machines to complete the task. In this question, we're asked how long it would take 6 machines...

(6)(X) = 60
X = 10 hours

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

ScottTargetTestPrep · Answer

Since 5 identical snow plows can clear an iced parking lot in 12 hours, the rate of the 5 plows is 1/12. To determine how long it would take 6 snow plows to clear the parking lot, we can create the following proportion in which x is the rate of the 6 plows:

5/(1/12) = 6/x

60 = 6/x

60x = 6

x = 1/10

Since the rate of the 6 plows is 1/10, the time it takes them to clear the iced parking lot is 1/(1/10) = 10 hours.

Answer: E

generis · Answer

If rate method is used, the trap is not calculating rate of ONE plow. One way to derive individual plow rate: alter RT=W formula slightly.

1) From given facts, find individual machine rate:

(# of plows) * R * T = W 
 5 * R * 12 = 1 
Rate of ONE plow,  R=\frac{1}{(5*12)}=\frac{1}{60}

2) Find time in new scenario: At that rate, time for 6 plows to finish is: 
 (# of plows) * R * T = W 
 6 * \frac{1}{60} * T = 1

TIME,  T =\frac{1}{(\frac{6}{60})}=(1 * \frac{60}{6})=(1*10)=10

Answer E

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5 identical snow plows can clear an iced parking lot in 12 h

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