Little Texas Drilling Company has three wells, each producing oil at a

Question

Little Texas Drilling Company has three wells, each producing oil at a constant rate. Well A produces one barrel every two minutes. Well B produces one barrel every three minutes. Well C produces one barrel every four minutes. How many hours does it take Little Texas Drilling Company to produce 165 barrels of oil?

(A) 2
(B) 3
(C) 4
(D) 18
(E) 180

Kudos for a correct solution.

(A) 2
(B) 3
(C) 4
(D) 18
(E) 180

KarishmaB · Accepted Answer

The way the question is worded and the options are given, you will round up.

How many hours does it take to produce 165 barrels of oil? You get 2.5 hours. 
So can you say that you can produce 165 barrels in 2 hours? No.
But can you say that you can produce 165 barrels in 3 hours? Yes. Even though some extra time is left but if you will be given round number hours only, you will need 3 hours.

With the same question and same options, even if you get 2.25 hours as the actual answer, you will still say you need 3 hours (the next closest integer) since 2 hrs are not enough.

NavenRk · Answer

The three rates of production are 0.5 barrels/min , 0.33 barrels/min & 0.25 barrels/min.

Lets consider the ans choices:

total no of barrels produced in

A) 2 hrs = 60+40+30 = 130
B) 3 hrs = 90+60+45 = 195

Hence B

Jackal · Answer

My attempt

Taking LCM of the 3 rates which is 12

This means in 12 minutes:
a produces 6 barrels
b produces 4 barrels
c produces 3 barrels

So after the first 12 mins total 13 barrels are produced when all a, b and c come back to starting position (notionally speaking).

Therefore 165/13 = 12 with a remainder of 9 barrels.
So total time is 12*12=144 plus the time required for 9 barrels.
If we manually check the sequence (as per the diagram) in 9 minutes 9 barrels are produced.
So total time taken for 165 barrels is 144+9=153 mins = 2 hours 33 mins

I go with option B in the current set of options.

kasturi72 · Answer

A produces 1 barrel every 2 mins so in 1 hr its 30 barrels
B produces 1 barrel in 3 mins so in 1 hr its 20 barrels 
C produces 1 barrel in 4 mins so in 1 hr its 15 barrels so total in 1 hr there are 65 barrels
 So in 2 hrs - 130 barrels and 3 hrs - 195 barrels

Will go with B

KarishmaB · Answer

You can also approximate to get the answer quickly.

Well A produces 1/2 a barrel per minute.
Wells B and C produce 1/3 + 1/4 = 7/12 (a little more than half) a barrel per minute.
So all three wells combined produce a little more than 1 barrel per minute. 
So for 165 barrels they will take a bit less than 165 mins which will be more than 2 hrs but less than 3 hrs.

Answer (B)

vishwaprakash · Answer

in 12 minutes 
A will produce 6, B - 4 and C - 3

Total 13 in 12 minutes.

13 barrel = 12 Minutes
165 barrel = (12/13)*165 Minutes
165 Barrel = (12/13)*(165/60) Hours
165 Barrel > 2 hours

Hence Option B,

ajdse22 · Answer

Thanks Karishma. So the answer is between 2 and 3 hours . I estimated (165*12)/13 to be roughly 150. This is right in the middle of 2 and 3, so how did you lean on 3 , which is choice B?

Luckisnoexcuse · Answer

A =1/2 barrel/min
B =1/3 barrel/min
C =1/4 barrel/min

A+ B + C = 13/12 barrel/min = 65 barrel/hr

165 barrels in 3 hr hence option B

JeffTargetTestPrep · Answer

We are given that well A produces one barrel every two minutes, well B produces one barrel every three minutes, and well C produces one barrel every four minutes. Since rate = work/time, well A’s rate = 1/2, well B’s rate = 1/3, and well C’s rate = 1/4.
 
If we let t = the time in minutes during which the wells work together, we can create the following equation to determine t:
 
(1/2)t + (1/3)t + (1/4)t = 165
 
Multiplying the entire equation by 12, we have:
 
6t + 4t + 3t = 1980
 
13t = 1980
 
t = 1980/13 = 152.3 minutes
 
Since 152.3 minutes = 2.54 hours, the correct answer choice is B.
 
Alternative solution:
 
Since well A produces one barrel every two minutes, it can produce 30 barrels in an hour. Likewise, since well B produces one barrel every three minutes and well C produces one barrel every four minutes, they can produce 20 and 15 barrels an hour, respectively. Thus, in one hour, these 3 wells can produce 30 + 20 + 15 = 65 barrels. Thus, it takes them 165/65 = 2.54 hours to produce 165 barrels.

Answer: B

exc4libur · Answer

r=td
rA=1/2; rB=1/3; rC=1/4
rA+rB+rC(t)=165
(1/2+1/3+1/4)t=165
t=165/(6+4+3/12)
t=165/13/12 mins / 60 = hrs
t=165*12/13*60=33/13=2+7/13>2.5~(3) hrs

Ans (B)

Rahuldg2000 · Answer

Hi,

Won't the 9 barrels take 1 min to make since the 3 wells are pumping independently.
In 1 minute, no. of barrels made = (2+3+4) i.e. A+B+C?

Little Texas Drilling Company has three wells, each producing oil at a

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