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Worker W produces n units in 5 hours~ Workers V and W, worki
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14 Jul 2020, 14:42
14 Jul 2020, 14:42
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72% (01:52) correct
27% (02:09) wrong based on 114 sessions
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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
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Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1141
Given Kudos: 9
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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
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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
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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!
