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

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Math Expert
Joined: 02 Sep 2009
Posts: 55631
Working together at their respective constant rates, robot A and robot  [#permalink]

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08 Jul 2018, 21:37
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Difficulty:

55% (hard)

Question Stats:

66% (02:30) correct 34% (03:17) wrong based on 91 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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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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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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09 Jul 2018, 05:57
2

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.

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

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09 Jul 2018, 07:07
1
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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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.

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

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03 Mar 2019, 15:44
Given: A+B rate * 6 minutes = 88 lbs
B rate = B, A rate = (3/5)*B
Question: 165 lbs / 3/5(B) = ? minutes

1) A+B rate * 1 minute = 88/6 lb

2) 88/6 = A+(3/5)A ---> 8/5A
A = 88/6 * 5/8 --> 55/6
55/6*3/5 = 11/2, rate of (3/5)A per minute

3) 165/11/2 = 30 minutes, E
Re: Working together at their respective constant rates, robot A and robot   [#permalink] 03 Mar 2019, 15:44
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