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A standard machine fills paint cans at a rate of 1 gallon ev
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14 Jun 2018, 14:41
14 Jun 2018, 14:41
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Question Stats:
88% (01:41) correct
11% (02:00) wrong based on 77 sessions
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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
(A) 1
(B) 1.5
(C) 2
(D) 2.5
(E) 3
Re: A standard machine fills paint cans at a rate of 1 gallon ev
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02 Jul 2018, 07:41
02 Jul 2018, 07:41
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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
(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 \(time = \frac{135}{45} = 3 hr\)
Re: A standard machine fills paint cans at a rate of 1 gallon ev
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07 Jul 2018, 04:35
07 Jul 2018, 04:35
Expert Reply
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
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
