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# When working together at their constant rates, machines A and B can

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Manager
Joined: 15 Feb 2018
Posts: 247
When working together at their constant rates, machines A and B can  [#permalink]

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13 Oct 2018, 04:41
00:00

Difficulty:

15% (low)

Question Stats:

75% (01:00) correct 25% (01:30) wrong based on 56 sessions

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When working together at their constant rates, machines A and B can complete a certain task in 4 hours. How many hours would it take machine B to complete the task, when working alone at its constant rate?

1) When working alone at its constant rate, machine A can finish the task in 6 hours.

2) When working alone at their respective rates, it takes machine B 6 hours longer than machine A to finish the task
Director
Joined: 19 Oct 2013
Posts: 508
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
Re: When working together at their constant rates, machines A and B can  [#permalink]

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13 Oct 2018, 05:19
1
1
philipssonicare wrote:
When working together at their constant rates, machines A and B can complete a certain task in 4 hours. How many hours would it take machine B to complete the task, when working alone at its constant rate?

1) When working alone at its constant rate, machine A can finish the task in 6 hours.

2) When working alone at their respective rates, it takes machine B 6 hours longer than machine A to finish the task

1/A + 1/B = (A+B)/A*B

This the combined rate 1 job in 4 hours

So it means 4 hours to finish 1 job.

We want to know B

Statement 1)

Tells us that 1/6 + 1/B = 1/4

1/4 - 1/6 = 1/B sufficient.

3/12 - 2/12 = 1/12. B takes 12 hours.

Statement 2)

1/A + 1/(A+6) = 1/4

We can find the value of A and therefore find the value of B.

Sufficient.

(A + A + 6)/(A^2 + 6A) = 1/4

4A + 4A + 24 = A^2 + 6A

A^2 - 2A - 24 = 0

(A - 6) (A + 4) = 0

A = 6
B = 12

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Re: When working together at their constant rates, machines A and B can   [#permalink] 13 Oct 2018, 05:19
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