 It is currently 26 Jun 2019, 01:48 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. Working together at their respective constant rates, robot A  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 120

Kudos [?]: 1910 , given: 397

Working together at their respective constant rates, robot A [#permalink]
Expert's post 00:00

Question Stats: 62% (02:15) correct 37% (02:24) wrong based on 16 sessions
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 $$\frac{3}{5}$$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
[Reveal] Spoiler: OA

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Director  Joined: 07 Jan 2018
Posts: 648
Followers: 7

Kudos [?]: 606 , given: 88

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

Machine B can do x work in 1 min
or, Machine B can do $$6x$$ work in $$6 min$$

It follows that Machine A is only 3/5 efficient as machine A hence,
Machine A can do $$\frac{18}{5} x work in 6 min.$$

From question,

$$\frac{18}{5} x + 6x = 88$$
because working together the two machines can polish $$88 pounds$$ of gemstone in $$6 min.$$

solving for x we get $$x = \frac{440}{48}$$
This is the pound of gemstone machine B can polish in 1 min.
The amount of gemstone that machine A can polish in 1 min is $$\frac{440}{48} * \frac{3}{5}$$
Hence, machine A can polish $$\frac{1320}{240}$$ pound of gemstone in 1 min.
or, Machine A can polish 1 pound of gemstone in $$\frac{240}{1320}$$ min
or, Machine A can polish 165 pound of gemstone in $$\frac{240}{1320} * 165$$ min = 30 min
_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 120

Kudos [?]: 1910  , given: 397

Re: Working together at their respective constant rates, robot A [#permalink]
1
KUDOS
Expert's post
Explanation

When rate problems involve multiple situations, it can help to set up an initial “skeleton” W= RT chart for the solution. That way, you can determine what data is needed and fill in that data as you find it. Since the question asks how long robot A will take alone, the chart will look like this:

Attachment: image1.jpg [ 26.04 KiB | Viewed 792 times ]

Work is known and the question asks for time, so robot A’s rate is needed. Call the rates a and b. Now set up another chart representing what you know about the two robots working together.

Attachment: image1.jpg [ 50.99 KiB | Viewed 791 times ]

Now, 6(a + b) = 88 and, from the question stem, robot A’s rate is $$\frac{3}{5}$$ of B’s rate. This can be written as $$a = \frac{3}{5}b$$. To solve for a, substitute for b:

$$a = \frac{3}{5} b$$
$$\frac{5}{3}a = b$$

$$6(a+ \frac{5}{3}a) = 88$$

$$6 \frac{8}{3} a = 88$$
$$a = \frac{11}{2}$$

So A’s rate is pounds per minute. Now just plug into the original chart:

Attachment: image1.jpg [ 28.05 KiB | Viewed 791 times ]

The time robot A takes to polish 165 pounds of gems is $$165/\frac{11}{2} =\frac{330}{165} = 30$$ minutes.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test Re: Working together at their respective constant rates, robot A   [#permalink] 10 Jul 2018, 06:12
Display posts from previous: Sort by

Working together at their respective constant rates, robot A  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.