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Machine A can produce balls at a constant rate of 2 balls per hour, an

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Machine A can produce balls at a constant rate of 2 balls per hour, an  [#permalink]

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New post 20 Mar 2018, 01:46
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[GMAT math practice question]

Machine A can produce balls at a constant rate of 2 balls per hour, and machine B can produce balls at a constant rate of 3 balls per hour. If at least one of machine A and machine B produces balls at any time, what is the smallest possible number of hours that machine A and machine B must work together at their constant rates to produce 70 balls in 20 hours?

A. 5hrs
B. 6hrs
C. 7hrs
D. 8hrs
E. 9hrs

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Re: Machine A can produce balls at a constant rate of 2 balls per hour, an  [#permalink]

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New post 20 Mar 2018, 03:05
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1
MathRevolution wrote:
[GMAT math practice question]

Machine A can produce balls at a constant rate of 2 balls per hour, and machine B can produce balls at a constant rate of 3 balls per hour. If at least one of machine A and machine B produces balls at any time, what is the smallest possible number of hours that machine A and machine B must work together at their constant rates to produce 70 balls in 20 hours?

A. 5hrs
B. 6hrs
C. 7hrs
D. 8hrs
E. 9hrs



Let them work together for X hours and B, the faster work for y hours

So I can make two equations..
1) x+y=20....3x+3y=60
2) 5x+3y=70

So we get 5x-3x=70-60=10.....x=5
So minimum is 5 hours..
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Re: Machine A can produce balls at a constant rate of 2 balls per hour, an  [#permalink]

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New post 20 Mar 2018, 05:15
MathRevolution wrote:
[GMAT math practice question]

Machine A can produce balls at a constant rate of 2 balls per hour, and machine B can produce balls at a constant rate of 3 balls per hour. If at least one of machine A and machine B produces balls at any time, what is the smallest possible number of hours that machine A and machine B must work together at their constant rates to produce 70 balls in 20 hours?

A. 5hrs
B. 6hrs
C. 7hrs
D. 8hrs
E. 9hrs


Lets go by options with minmum given time -

A. 5 = a & b can produce 25 balls working together in 5 Hours. The remaining 45 balls can be produced by Machine B working for 15 Hours.

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Re: Machine A can produce balls at a constant rate of 2 balls per hour, an  [#permalink]

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New post 20 Mar 2018, 07:59
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MathRevolution wrote:
[GMAT math practice question]

Machine A can produce balls at a constant rate of 2 balls per hour, and machine B can produce balls at a constant rate of 3 balls per hour. If at least one of machine A and machine B produces balls at any time, what is the smallest possible number of hours that machine A and machine B must work together at their constant rates to produce 70 balls in 20 hours?

A. 5hrs
B. 6hrs
C. 7hrs
D. 8hrs
E. 9hrs


Machine A's rate - 2 balls/hr
Machine B's rate - 3 balls/hr

Together, the machines produce 5 balls in an hour.
If the machines need to produce 70 balls in 20 hours, in order to use both the machines
for the smallest number of hours(let's call it x), we need to use Machine B for the rest of
the time

5x + 3(20 - x) = 70
5x + 60 - 3x = 70
2x = 10 -> x = 5

Therefore, the smallest possible number of hours both the machines work together is 5(Option A)
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Re: Machine A can produce balls at a constant rate of 2 balls per hour, an  [#permalink]

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New post 22 Mar 2018, 15:49
MathRevolution wrote:
[GMAT math practice question]

Machine A can produce balls at a constant rate of 2 balls per hour, and machine B can produce balls at a constant rate of 3 balls per hour. If at least one of machine A and machine B produces balls at any time, what is the smallest possible number of hours that machine A and machine B must work together at their constant rates to produce 70 balls in 20 hours?

A. 5hrs
B. 6hrs
C. 7hrs
D. 8hrs
E. 9hrs


To minimize the time both the machines are working together, we must maximize the time that the faster of the two machines, machine B, works alone. Let’s assume that machine B works for the entire 20 hours, producing 20 x 3 = 60 balls. The remaining 70 - 60 = 10 balls must be produced by machine A, and it will take 10 / 2 = 5 hours for machine A to produce them. Thus, the two machines must work for a minimum of 5 hours together.

Answer: A
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Re: Machine A can produce balls at a constant rate of 2 balls per hour, an  [#permalink]

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New post 22 Mar 2018, 17:54
=>

Since machine B has the faster working rate, it must work for the entire period to minimize the number of hours that machine A has to work.
When machine B works for 20 hours, it produces 60 balls. This means that machine A must produce 70 – 60 = 10 balls, and it must work for 5 hours, since the work rate of machine A is 2 balls per hour.

Therefore, the answer is A.

Answer: A
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Re: Machine A can produce balls at a constant rate of 2 balls per hour, an  [#permalink]

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New post 15 May 2018, 15:55
Algebraic approach:

Let's imagine that both machines were working together with combined speed 5 balls/h and then B(slowest) stopped, so they have produced X balls. After that machine A is working alone 3 balls/h and will produce 70-X balls. And total time of both iterations is 20 h. So we get an equation:

x/5 + (70-x)/3 = 20, X=25, so the time they have to work together is x/5 = 25/5 = 5. Answer (A)
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Re: Machine A can produce balls at a constant rate of 2 balls per hour, an &nbs [#permalink] 15 May 2018, 15:55
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