A carpenter worked alone for 1 day on a job that would take him 6 more

A carpenter worked only 1 day on something that takes him 6 MORE days.
Means;
Carpenter finishes his work in 7 days.
Let his buddy finish the same task in x days.

Respective rates per day:
1/7 AND 1/x

To complete 1 work:
First guy worked for 5 days @ rate=1/7 per day.
Second one worked for 4 days @ rate=1/x per day

Expression:
Days*Rate=Work
5*1/7+4*1/x=1
5x+28=7x
2x=28
x=14 days.

Ans: "D"

the speed of first carpenter\(=\frac{1}{7}\)
the speed of second carpenter\(=\frac{1}{X}\)

\(1*\frac{1}{7}+4*(\frac{1}{7}+\frac{1}{X})=1\)

\(\frac{4}{7}+\frac{4}{X}=\frac{6}{7}\)

\(X=14\)

First carpenter can finish the job in 7 days. After first day carpentar 2 joins and the work gets completed in 5 days.

Let the total work be 35 units. (LCM of 5 & 7) Rate of carpentar 1 = 35/7 = 5 units per day. He works for 5 days , so he does total of 25 units out of 35 units. That means carpentar 2 does 35-25 units = 10 units in 4 days. so rate of carpentar 2 - 10/4 = 2.5 units per day. So he will do complete work in 35/2.5 = 14 days.

Carpenter takes 1+6 = 7days
When he was joined by his fellow carpenter i.e. after 1 day \(\frac{1 ^t^h}{7}\) of the work was already done so remaining \(\frac{6^t^h}{7}\) was done together in 4 days . setting this up on equation .

\(\frac{1}{7} + \frac{1}{X} = \frac{6}{7} * \frac{1}{4}\)
X=14
Answer D .

Nicely explained Fluke

1.(no.of days worked by the first person)/ time taken by him if working alone + (no.of days worked by the second person)/ time taken by him if working alone=1
2. (5/7)+ (4/x) = 1, So x=14

Fascinatingggggggggggg

On 1st day one carpenter did = 1/7th work (Total days required to finish work= 7 days

Remaining work = 6/7

In next 4 days 1st carpenter must have done 4/7 work, leaving 6/7-4/7= 2/7 for 2nd carpenter.

Now, if 2nd carpenter does 2/7 work in 4 days. he requires 4*7/2= 14 days to finish the whole task.

D is the answer

The rate of the first carpenter is 1/7.

Since the two carpenters can complete the remaining 6/7 of the job in 4 days, their combined rate is:

(6/7)/4 = 6/28 = 3/14

We can let x = the number of days it takes the second carpenter to complete the job alone; thus, his rate = 1/x. We can create the following equation:

1/7 + 1/x = 3/14

Multiplying the equation by 14x, we have:

2x + 14 = 3x

14 = x

The second carpenter could complete the job alone in 14 days.

Answer: D

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

A's rate is 1/7, he worked for 1 day and did 1*1/7=1/7 work;
B's rate is 1/X, he worked with A for 4 days 4*(1/7 + 1/X) work;

Now if we combine them both we'll get completed job:
1/7 + 4*(1/7 + 1/X) = 1; => (4(X+7))+X)/7X = 1;
5X + 28 = 7X; => X = 14;

Let time taken for second carpenter to complete the job working alone is B days

so, as per the given question, equation is as follows.

1/7 + (1/7+1/B) *4 =1

Solve for B, answer is 14.

Given that the first carpenter would have completed the work in 7 days. His rate of work per day = \(\frac{W}{7}\)

Since after working for 1 day he started working with another person and got the work done in 4 more days.

In these 5 days, he completed a total work of\( \frac{5W}{7}\)

The other person in the 4 days completed the remaining: \(W\ -\ \frac{5W}{7}=\ \frac{2W}{7}\) part of work in 4 days.

His rate of work is: \(\frac{W}{14}\)

It would take 14 days alone for him to complete the work.

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