GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Worker W produces n units in 5 hours~ Workers V and W, worki
[#permalink]
14 Jul 2020, 14:42
14 Jul 2020, 14:42
2
Expert Reply
6
Bookmarks
00:00
Question Stats:
72% (01:49) correct
27% (02:11) wrong based on 111 sessions
Hide Show timer Statistics
Worker W produces n units in 5 hours Workers V and W, working independently but at the same time, produce n units in 2 hours. How long would it take V alone to produce n units?
(A) 1 hr 26 min
(B) 1 hr 53 min
(C) 2 hr 30 min
(D) 3 hr 20 min
(E) 3 hr 30 min
Kudos for the right answer and explanation
(A) 1 hr 26 min
(B) 1 hr 53 min
(C) 2 hr 30 min
(D) 3 hr 20 min
(E) 3 hr 30 min
Kudos for the right answer and explanation
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: Worker W produces n units in 5 hours~ Workers V and W, worki
[#permalink]
15 Jul 2020, 06:07
15 Jul 2020, 06:07
3
This problem is based on Work Rate Concept.
We will be using two concepts\formulas in this problem:
1. Rate * Time = Work Done
2. When two people work together then their rates get added up.
Let Rate of W is "W" and Rate of V is "V"
Worker W produces n units in 5 hour
Using, Rate * Time = Work Done we have
W * 5 = n => W = \(\frac{n}{5}\) ...(1)
Workers V and W, working independently but at the same time, produce n units in 2 hours
=> (V + W) * 2 = n [ as V and W are working together so their rates will get added up ]
=> V + W = \(\frac{n}{2}\) ....(2)
(2) - (1) we have
V + W - W = \(\frac{n}{2}\) - \(\frac{n}{5}\) = \(\frac{5n}{10}\) - \(\frac{2n}{10}\)
=> V = \(\frac{3n}{10}\)
How long would it take V alone to produce n units
V * t = n
=> \(\frac{3n}{10}\) * t = n
=> t = \(\frac{10}{3}\)hrs = \(\frac{10 * 60}{3}\) mins = 200 mins = 3hrs 20mins
So, answer will be D
Hope it helps!
We will be using two concepts\formulas in this problem:
1. Rate * Time = Work Done
2. When two people work together then their rates get added up.
Let Rate of W is "W" and Rate of V is "V"
Worker W produces n units in 5 hour
Using, Rate * Time = Work Done we have
W * 5 = n => W = \(\frac{n}{5}\) ...(1)
Workers V and W, working independently but at the same time, produce n units in 2 hours
=> (V + W) * 2 = n [ as V and W are working together so their rates will get added up ]
=> V + W = \(\frac{n}{2}\) ....(2)
(2) - (1) we have
V + W - W = \(\frac{n}{2}\) - \(\frac{n}{5}\) = \(\frac{5n}{10}\) - \(\frac{2n}{10}\)
=> V = \(\frac{3n}{10}\)
How long would it take V alone to produce n units
V * t = n
=> \(\frac{3n}{10}\) * t = n
=> t = \(\frac{10}{3}\)hrs = \(\frac{10 * 60}{3}\) mins = 200 mins = 3hrs 20mins
So, answer will be D
Hope it helps!
Re: Worker W produces n units in 5 hours~ Workers V and W, worki
[#permalink]
17 Jul 2020, 04:45
17 Jul 2020, 04:45
1
Hello! This problem can easily be understood and solved by assuming real numbers instead of trying to solve it with variable.
Let's assume n = 10
=> Rate(w) = 10 Units / 5 Hours
AND
Rate (w,v) = 10 Units / 2 Hours
So, R(w,v) = R(w) + R(v)
=> 10/2 = 10/5 + R(v)
=> R(v) = 10/2 - 10/5 =
=> R(v) = 3/1 (3 Units per Hour)
Now, Set up a proportion: R(v) = 3 Units / 1 Hours = 10 Units / t Hours
=> t = 10 / 3 Hours
=> t = 3 + 1/3 Hours
=> t = 3 Hours 20 Minutes
Hence, D
I hope it helps!
Godspeed!
Let's assume n = 10
=> Rate(w) = 10 Units / 5 Hours
AND
Rate (w,v) = 10 Units / 2 Hours
So, R(w,v) = R(w) + R(v)
=> 10/2 = 10/5 + R(v)
=> R(v) = 10/2 - 10/5 =
=> R(v) = 3/1 (3 Units per Hour)
Now, Set up a proportion: R(v) = 3 Units / 1 Hours = 10 Units / t Hours
=> t = 10 / 3 Hours
=> t = 3 + 1/3 Hours
=> t = 3 Hours 20 Minutes
Hence, D
I hope it helps!
Godspeed!
