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Little Texas Drilling Company has three wells, each producin

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Little Texas Drilling Company has three wells, each producin

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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

OA B

Source: Magoosh

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BTGmoderatorDC wrote:
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

OA B

Source: Magoosh
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 = 195

Multiplying the entire equation by 12, we have:

6t + 4t + 3t = 2340

13t = 2340

t = 2340/13 = 180 minutes, or 3 hours.


Alternate 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 195/65 = 3 hours to produce 195 barrels.

Answer: B

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

Let's consider the answer choices:

The total number of barrels produced in

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

Hence B

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Given the answer choices, the prompt should read as follows:

BTGmoderatorDC wrote:
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 185 barrels of oil?

(A) 2
(B) 3
(C) 4
(D) 18
(E) 180
A's rate = (1 barrel)/(2 minutes) * (60 minutes)/(1 hour) = 30 barrels per hour.
B's rate = (1 barrel)/(3 minutes) * (60 minutes)/(1 hour) = 20 barrels per hour.
C's rate = (1 barrel)/(15 minutes) * (60 minutes)/(1 hour) = 15 barrels per hour.
Since the combined rate for A+B+C = 30+20+15 = 65 barrels per hour, the time to produce 185 barrels = w/r = 185/65 = 3 hours.

The correct answer is B.

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