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

Question

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 2/3
B) 7
C) 9
D) 14
E) 24

A) 4 2/3
B) 7
C) 9
D) 14
E) 24

KarishmaB · Accepted Answer

This is how I would deal with this problem:

Rate of work of first carpenter = 1/7 work/day
Both, working together, took 4 days to complete (6/7)th of the work.
So they will take 4*7/6 (= 14/3 days) to complete the full work.

Rate of work of both together = 3/14 work/day

Mind you, working alone, first carpenter does 1/7 = 2/14 work/day
Together, they complete 3/14 work/day. So the second carpenter must be doing 1/14 work/day.
So working alone, he will take 14 days.

Spidy001 · Answer

it takes 7 days for carpenter 1 to complete the work.

=> rate of carpenter1 = 1/7

=> amount of work done by carpenter1 on first day = 1/7

rest of 6/7 work is done both by carpenter1 and carpenter2 in 4 days

=> 1/7+rate of carpenter2 = (6/7)/4
=> rate of carpenter2 = 1/14

=> carpenter2 alone can finish this work in 14 days.

Answer is D.

fluke · Answer

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"

Aj85 · Answer

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.

pike · Answer

Nicely explained Fluke

shahideh · Answer

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

mahdiir · Answer

Fascinatingggggggggggg

Lucky2783 · Answer

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 .

Divyadisha · Answer

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

SVaidyaraman · Answer

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

JeffTargetTestPrep · 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

BrentGMATPrepNow · Answer

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

mm229966 · Answer

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;

VIGHNESHKAMATH · Answer

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.

GmatPoint · Answer

﻿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.

horrorslive · Answer

Bunuel   chetan2u   KarishmaB  
Doesn't 4 more days mean 5 days? So together won't they complete the remaining job in 5 days?

KarishmaB · Answer

The first carpenter worked alone for 1 day.  He and another carpenter completed the job in 4 more days

This means the two worked together for 4 days. The word "more" is used to indicate that they worked for 4 days after the first carpenter worked alone for 1 day.

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

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