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cat2010
Joined: 26 Nov 2022
Last visit: 18 Mar 2023
Posts: 106
Given Kudos: 12
Location: India
Schools: Foster '25 Northeastern Ross '25 UT Dallas
GMAT 1: 700 Q46 V40
GPA: 3.8
11 Jan 2023, 18:57
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
71% (02:36) correct
29%
(03:00)
wrong
based on 385
sessions
History
Date
Time
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Not Attempted Yet
Steve can paint his greenhouse in 4 hours 40 minutes minutes, working alone; his brother Phil can do the same job in 6 hours, working alone. If they work together, to the nearest minute, how long will it take them?
A.2 hours 38 minutes
B.2 hours 54 minutes
C.2 hours 22 minutes
D.2 hours 42 miutes
E.3 hours
A.2 hours 38 minutes
B.2 hours 54 minutes
C.2 hours 22 minutes
D.2 hours 42 miutes
E.3 hours
14 Jan 2023, 10:33
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Given that Steve can paint his greenhouse in 4 hours 40 minutes minutes, working alone; his brother Phil can do the same job in 6 hours, working alone. If they work together, to the nearest minute, how long will it take them?
Let Rate of Steve be S, Rate of Phil be P.
We will be using Rate * Time = Work done formula.
Since work done is same so we will take work done as 1
Steve can paint his greenhouse in 4 hours 40 minutes minutes, working alone
=> 4 hours 40mins = 4*60 + 40 mins = 280 mins
=> S * 280 = 1
=> S = \(\frac{1}{280}\) ...(1)
Phil can do the same job in 6 hours, working alone
=> 6 hours = 6*60mins = 360 mins
=> P * 360 = 1
=> P= \(\frac{1}{360}\) ...(2)
How long will it take both of them working together to finish the work
=> Combined Rate = S + P = \(\frac{1}{280}\) + \(\frac{1}{360}\) = \(\frac{1}{40*7}\) + \(\frac{1}{40*9}\)
= \(\frac{9 + 7}{40*7*9}\) = \(\frac{16}{40*7*9}\) = \(\frac{2}{315}\)
=> (S + P) * Time = 1
=> \(\frac{2}{315}\) * Time = 1
=> Time = \(\frac{315}{2}\) = 157.5 mins ~ 120 + 38 mins = 2 hours 38 minutes
So, Answer will be A
Hope it helps!
Watch the following video to learn How to Solve Work Rate Problems
Let Rate of Steve be S, Rate of Phil be P.
We will be using Rate * Time = Work done formula.
Since work done is same so we will take work done as 1
Steve can paint his greenhouse in 4 hours 40 minutes minutes, working alone
=> 4 hours 40mins = 4*60 + 40 mins = 280 mins
=> S * 280 = 1
=> S = \(\frac{1}{280}\) ...(1)
Phil can do the same job in 6 hours, working alone
=> 6 hours = 6*60mins = 360 mins
=> P * 360 = 1
=> P= \(\frac{1}{360}\) ...(2)
How long will it take both of them working together to finish the work
=> Combined Rate = S + P = \(\frac{1}{280}\) + \(\frac{1}{360}\) = \(\frac{1}{40*7}\) + \(\frac{1}{40*9}\)
= \(\frac{9 + 7}{40*7*9}\) = \(\frac{16}{40*7*9}\) = \(\frac{2}{315}\)
=> (S + P) * Time = 1
=> \(\frac{2}{315}\) * Time = 1
=> Time = \(\frac{315}{2}\) = 157.5 mins ~ 120 + 38 mins = 2 hours 38 minutes
So, Answer will be A
Hope it helps!
Watch the following video to learn How to Solve Work Rate Problems
06 Oct 2025, 05:45
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