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21 Aug 2021, 02:37
Kudos
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D
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:
72% (03:13) correct
28%
(03:11)
wrong
based on 158
sessions
History
Date
Time
Result
Not Attempted Yet
Ross can paint the walls of his dormitory in 12 hours. His friends, Ryan and Jack, each working alone can paint the same walls in 15 hours and t hours, respectively. On Sunday morning Ross starts to paint his dormitory walls alone and 4 hours later Ryan joins him. After another 4 hours Jack joins them. After that Ross, Ryan, and Jack together paint the wall in 20 minutes. What is the value of t?
A. 4 hours
B. 8.5 hours
C. 15 hours
D. 20 hours
E. 25 hours
A. 4 hours
B. 8.5 hours
C. 15 hours
D. 20 hours
E. 25 hours
21 Aug 2021, 03:06
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antoniogmat
Ross works for total 4+4 hrs + 20 minutes = 4+4+(1/3)=25/3 hrs
If Ross can finish the work in 12 hrs, he would complete \(\frac{1}{12}*\frac{25}{3}=\frac{25}{36}\) in 25/3 hrs.
Ryan works for total 4 hrs + 20 minutes = 4+(1/3)=13/3 hrs
If Ryan can finish the work in 15 hrs, he would complete \(\frac{1}{15}*\frac{13}{3}=\frac{13}{45}\) in 25/3 hrs.
Total work done by both Ross and Ryan combined = \(\frac{25}{36}+\frac{13}{45}=\frac{177}{180}\)
Thus Jack does \(1-\frac{177}{180}=\frac{3}{180}=\frac{1}{60}\) in 1/3 hours.
Or, Jack’s one hour work = \(\frac{1}{60}*3=\frac{1}{20}\)
Time taken to complete the entire work, therefore, is 20 hours.
D
21 Aug 2021, 09:27
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antoniogmat
After the first four hours, Ross completed \(\frac{4}{12} = \frac{1}{3}\) of the job.
For the next four hours, Ross and Ryan complete \(\frac{4}{12} + \frac{4}{15} = \frac{9}{15} = \frac{3}{5}\) of the job.
Therefore for the final 20 minutes, there is \(1 - \frac{1}{3} - \frac{3}{5} = \frac{1}{15}\) of the job undone.
Their combined rate is \(\frac{1}{12} + \frac{1}{15} + \frac{1}{t}\) and they do the rest of the job in 20 min. Therefore:
\((\frac{1}{12} + \frac{1}{15} + \frac{1}{t})*\frac{1}{3} = \frac{1}{15}\).
\(\frac{1}{t} = \frac{1}{5} - \frac{9}{60} = \frac{3}{60} = \frac{1}{20}\).
\(t = 20\).
Ans: D
