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# A standard machine fills paint cans at a rate of 1 gallon ev

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Joined: 07 Jun 2014
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A standard machine fills paint cans at a rate of 1 gallon ev [#permalink]  14 Jun 2018, 14:41
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Question Stats:

69% (01:21) correct 30% (01:11) wrong based on 13 sessions
A standard machine fills paint cans at a rate of 1 gallon every 4 minutes. A deluxe machine fills gallons of paint at twice the rate of a standard machine. How many hours will it take a standard machine and a deluxe machine, working together, to fill 135 gallons of paint?

(A) 1
(B) 1.5
(C) 2
(D) 2.5
(E) 3
[Reveal] Spoiler: OA

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Sandy
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Joined: 20 Apr 2016
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Re: A standard machine fills paint cans at a rate of 1 gallon ev [#permalink]  02 Jul 2018, 07:41
sandy wrote:
A standard machine fills paint cans at a rate of 1 gallon every 4 minutes. A deluxe machine fills gallons of paint at twice the rate of a standard machine. How many hours will it take a standard machine and a deluxe machine, working together, to fill 135 gallons of paint?

(A) 1
(B) 1.5
(C) 2
(D) 2.5
(E) 3

Here ,

The standard machine rate = $$\frac{1}{4} *60 minutes = 15 gallons/ hr$$

The deluxe machine rate = $$2 * standard machine rate = 30 gallons/hr$$

Therefore working together they fills = $$15 + 30 = 45 gallons/hr$$

Now to fill 135 gallons of paint

We know $$Work = Rate * Time$$

or $$135 = 45 * time$$

or $$time = \frac{135}{45} = 3 hr$$
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1776 [0], given: 397

Re: A standard machine fills paint cans at a rate of 1 gallon ev [#permalink]  07 Jul 2018, 04:35
Expert's post
Explanation

The question asks for the amount of time in hours, convert the work rates from gallons per minute to gallons per hour. First, calculate the rate of the standard machine:

$$\frac{1..gallon}{4..minutes} \times \frac{60..minutes}{1..hour}=15$$ gallons per hour.

Since the deluxe machine’s rate is twice the standard machine’s rate, the deluxe machine can fill 15 × 2 = 30 gallons of paint per hour. Together, the machines can fill 15 + 30 = 45 gallons of paint per hour. Now apply the formula for work, W = RT:

135 = 45 × T

3 = T
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Re: A standard machine fills paint cans at a rate of 1 gallon ev   [#permalink] 07 Jul 2018, 04:35
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