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Working together at their respective constant rates, robot A and robot

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Working together at their respective constant rates, robot A and robot  [#permalink]

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New post 08 Jul 2018, 21:37
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  45% (medium)

Question Stats:

67% (02:03) correct 33% (02:49) wrong based on 63 sessions

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Working together at their respective constant rates, robot A and robot B polish 88 pounds of gemstones in 6 minutes. If robot A’s rate of polishing is 3/5 that of robot B, how many minutes would it take robot A alone to polish 165 pounds of gemstones?

(A) 15.75
(B) 18
(C) 18.75
(D) 27.5
(E) 30

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Re: Working together at their respective constant rates, robot A and robot  [#permalink]

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New post 08 Jul 2018, 22:18
Given that \(\frac{1}{A}\) + \(\frac{1}{B}\) = \(\frac{1}{6}\).....(1)
And aslo given that A = \(\frac{3}{5}\)B.......(2)
Now, substituting (2) in (1) and simplifying, we get B =16min and A = 9.6min (This is the time taken by individual robots to polish 88 pounds)
Now for 165 pounds. The time taken by A is \(\frac{165*9.6}{88}\) = 18min.
Ans is B

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Working together at their respective constant rates, robot A and robot  [#permalink]

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New post 08 Jul 2018, 22:50
Bunuel wrote:
Working together at their respective constant rates, robot A and robot B polish 88 pounds of gemstones in 6 minutes. If robot A’s rate of polishing is 3/5 that of robot B, how many minutes would it take robot A alone to polish 165 pounds of gemstones?

(A) 15.75
(B) 18
(C) 18.75
(D) 27.5
(E) 30


Since Robot A works at \(\frac{3}{5}(60\)%) the rate at which Robot B works, together they do work of \(1.6(1+.6)\) robots.

1.6 robots polish 88 pounds in 6 minutes. In 6 minutes, Robot A(0.6 robot) polishes \(\frac{88}{1.6}*0.6\) or 33 pounds of gemstones.

Therefore, it will take Robot A (\(\frac{165}{33} = 5\)) 6 minute intervals = 30(Option E) minutes to polish 165 pounds of gemstones.
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Re: Working together at their respective constant rates, robot A and robot  [#permalink]

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New post 09 Jul 2018, 05:57
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Solution



Given:
    • Working together at their respective constant rates, robot A and robot B polish 88 pounds of gemstones in 6 minutes
    • Robot A’s rate of polishing is \(\frac{3}{5}\) that of robot B

To find:
    • How many minutes would it take robot A alone to polish 165 pounds of gemstones

Approach and Working:
If robot B polishes x gemstones per minute, then robot A polishes \(\frac{3x}{5}\) gemstones per minute
    • Therefore, in 6 minutes, they can polish \(6 (x + \frac{3x}{5}) = 6 * \frac{8x}{5}\) gemstones
    • Or we can write, \(6 * \frac{8x}{5} = 88\)
    Or, \(x = 88 * \frac{5}{6} * 8 = \frac{55}{6}\) gemstones/minute

Therefore, in 1 minute, robot A can polish = \(\frac{55}{6} * \frac{3}{5} = \frac{11}{2}\) gemstones = 5.5 gemstones
    • Hence, to polish 165 gemstones, robot A will take \(\frac{165}{5.5} = 30\) minutes

Hence, the correct answer is option E.

Answer: E
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Re: Working together at their respective constant rates, robot A and robot  [#permalink]

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New post 09 Jul 2018, 07:07
Bunuel wrote:
Working together at their respective constant rates, robot A and robot B polish 88 pounds of gemstones in 6 minutes. If robot A’s rate of polishing is 3/5 that of robot B, how many minutes would it take robot A alone to polish 165 pounds of gemstones?

(A) 15.75
(B) 18
(C) 18.75
(D) 27.5
(E) 30

Let , Efficiency of Robot B = 5e
So, Efficiency of Robot A = 3e

Combined efficiency of A and B is 8e = \(\frac{88}{6}\) pounds/min

Or, e = \(\frac{11}{6}\) pounds/min

So, Efficiency of A = \(\frac{33}{6}\) pound/min

Thus, Time taken for robot A to polish 165 gemstones is \(\frac{165*6}{33}\) = 30 minutes, Answer must be (E)
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Re: Working together at their respective constant rates, robot A and robot  [#permalink]

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New post 13 Jul 2018, 23:24
Soln: Working together - A+B = 88 in 6 mins.

A = 3/5 B

3/5B+B = 88

3B+5B = 88 * 5

8B = 440 ; B = 55 i.e - B polishes 55 pounds in 6 mins , Rate of B = 55 / 6 per min.

A = 3/5 B

A = 3/5 * 55/6 = 11/2 pound/min

W = Rate * Time

Time = Work / Rate

Time for A = 165 / (11/2) = 330/11 = 30 Mins.

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Re: Working together at their respective constant rates, robot A and robot &nbs [#permalink] 13 Jul 2018, 23:24
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