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

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A standard machine fills paint cans at a rate of 1 gallon ev [#permalink] New post 14 Jun 2018, 14:41
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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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Re: A standard machine fills paint cans at a rate of 1 gallon ev [#permalink] New post 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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Retired Moderator
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Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 173

Kudos [?]: 2971 [0], given: 394

Re: A standard machine fills paint cans at a rate of 1 gallon ev [#permalink] New post 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] New post 09 Jul 2019, 05:45
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



Easy way:
SD M. >>> 1gln = 4min.
Dl M. >>> 2gln = 4min.

Total 3gln = 4min. (As they work together same time)
So 1gln = 4/3 min.
and 135g = 4*135/3 (min) = 180/60 (hour) = 3 hour.

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Re: A standard machine fills paint cans at a rate of 1 gallon ev   [#permalink] 09 Jul 2019, 05:45
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