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A carpenter worked alone for 1 day on a job that would take him 6 more
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10 Nov 2021, 03:58
10 Nov 2021, 03:58
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A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 4 more days. How many days would it have taken the second carpenter to do the complete job working alone?
A) \(4 \frac{2}{3}\)
B) 7
C) 9
D) 14
E) 24
A) \(4 \frac{2}{3}\)
B) 7
C) 9
D) 14
E) 24
Re: A carpenter worked alone for 1 day on a job that would take him 6 more
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11 Nov 2021, 03:32
11 Nov 2021, 03:32
1
Carpenter 1 take 7 days in total to complete the job
rate of working of carpenter 1, \(r_1 = \frac{1}{7}\)
Carpenter 1 worked for 1 day, which means he completed \(\frac{1}{7}\)th of the job
Remaining job = \(\frac{6}{7}\)th
Carpenter 1 and Carpenter 2 completed the remaining job in 4 days
Let \(r_2\) be the rate of working of Carpenter 2
\(\frac{6}{7} = (r_1 + r_2)4\)
\(\frac{6}{7} = (\frac{1}{7} + r_2)4\)
\(\frac{3}{14} = \frac{1}{7} + r_2\)
\(r_2 = \frac{3}{14} - \frac{1}{7} = \frac{3}{14} - \frac{2}{14} = \frac{3-2}{14} = \frac{1}{14}\)
Which means Carpenter 2 would take \(\frac{1}{r_2} = \) 14 days to complete job alone
Hence, Answer is D
rate of working of carpenter 1, \(r_1 = \frac{1}{7}\)
Carpenter 1 worked for 1 day, which means he completed \(\frac{1}{7}\)th of the job
Remaining job = \(\frac{6}{7}\)th
Carpenter 1 and Carpenter 2 completed the remaining job in 4 days
Let \(r_2\) be the rate of working of Carpenter 2
\(\frac{6}{7} = (r_1 + r_2)4\)
\(\frac{6}{7} = (\frac{1}{7} + r_2)4\)
\(\frac{3}{14} = \frac{1}{7} + r_2\)
\(r_2 = \frac{3}{14} - \frac{1}{7} = \frac{3}{14} - \frac{2}{14} = \frac{3-2}{14} = \frac{1}{14}\)
Which means Carpenter 2 would take \(\frac{1}{r_2} = \) 14 days to complete job alone
Hence, Answer is D
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Re: A carpenter worked alone for 1 day on a job that would take him 6 more
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11 Nov 2021, 08:06
11 Nov 2021, 08:06
2
GeminiHeat wrote:
A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 4 more days. How many days would it have taken the second carpenter to do the complete job working alone?
A) \(4 \frac{2}{3}\)
B) 7
C) 9
D) 14
E) 24
A) \(4 \frac{2}{3}\)
B) 7
C) 9
D) 14
E) 24
A straightforward approach is to assign a nice value to the job.
We're looking for a number that works well with the given numbers (7 days to complete the job, and 4 extra days with help).
So let's say the carpentry job consists of making 56 wooden widgets
GIVEN: A carpenter worked alone for 1 day on a job that would take him 6 more days to finish.
This tells us that it would take the carpenter 7 days to make 56 wooden widgets
So, in ONE day, the carpenter can make 8 wooden widgets.
So, after the first day, the number of widgets we still need to make = 56 - 8 = 48
GIVEN: He and another carpenter completed the job in 4 more days.
So the two carpenters we're able to make 48 wooden widgets in 4 days
This means their COMBINED rate is 12 widgets per day
We already know that the FIRST carpenter makes 8 wooden widgets per day
This means the SECOND carpenter can make 4 wooden widgets per day.
QUESTION: How many days would it have taken the second carpenter to do the complete job working alone?
The job consists of making 56 wooden widgets
The SECOND carpenter can make 4 wooden widgets per day
time = output/rate
So, time = 56/4 = 14 days
Answer: D
Cheers,
Brent
