A,B,C working alone finish constructing a house in 4, 6 and 12 hrs. re

Question

A, B, C working alone finish constructing a house in 4, 6 and 12 hrs. resp. A starts alone and works for 1 hr. He is then joined by B and they work together for 1 hr. Finally C joins them and they all work together to finish the work. If they start working at 9 am, at what time will they finish?

A. 11.30 am
B. 11.40 am.
C. 12.00 pm
D.11.10 am
E. 11.20am

A. 11.30 am 
B. 11.40 am. 
C. 12.00 pm 
D.11.10 am 
E. 11.20am

Let's take the LCM of 4,6, and 12. LCM = 36
 We know,
 R* T = W 
(For A) R * 4 = 36 R =9
(For B) R * 6 = 36 R =6 
(For C) R * 12 = 36 R =3
A+B+C combined rate = 18
Now,
A completes 9 hrs of work in 1 hour. A and B combined completes 9+6 hrs of work in 1 hour. Total work completed is 24. Remaining work is 36-24 = 12.
Rate of A+B+C = 18. 
Therefore, 
R * T = W ==> 18 * t = 12 ==> t = 12/18 = 2/3hrs   
40 min + 1+1 hour = 2 hour 40 min.

therefore, answer is b. 
 
Is this a sub-600 level question?

Abhishek009 · Answer

Let the total work be 12 units Efficiency of A = 3 units/ hour Efficiency of B = 2 units/ hour Efficiency of C = 1 units/ hour So, A completes 3 units of work by 10 am So, A and B completes 5 units of work by 11 am Work left is 4 units ( 12 - 3 - 5 ) and combined efficiency of A, B and C is 6 units So, time required to complete 4 units will be 4/6 => 4/6*60 = 40 minutes... So they will require 40 minutes after 11 am to complete the remaining work... Hence answer will be (B) 11:40 am :lol:

This problem doesn't require the use of the formula R* T = W So do not involve in the concept of RTW unnecesarily

Divyadisha · Answer

A's 1 hr work= 1/4
B's 1 hr work= 1/6
C's 1hr work= 1/12

A+B+C's 1 hr work = 1/4 +1/6+1/12= 1/2

Now A worked alone for 1 hr. That means he did 1/4th of the work.
A and B worked together for 1 hr. So, they both did 1/4+1/6= 10/24 of the total work.

After 2 hrs the total work done was= 1/4 +10/24= 16/24

And, the remaining work was= 8/24= 1/3

All three of them did 1/3 work together.
If they do 1/2 work in 1 hr, they will do 1/3 work in 2/3*60= 40 mins

Total time taken to finish the job
1hr +1hr+40 mins= 2hr 40 mins

They will finish the job at 11:40 am.

IMHO, this is not a sub 600 level question.

KarishmaB · Answer

Say they work for t fraction of an hour after 11.

(Rate*Time) for each = (2 + t)/4 + (1 + t)/6 + t/12 = 1 = Total Work

6t/12 = 1/3

t = 2/3 hrs = 40 mins

Time at which the work gets done = 11:40

Alex75PAris · Answer

From the question we know :

Ra x 4 = 1 => Ra = 1/4
Rb x 6 = 1 => Rb = 1/6
Rc x 12 = 1 => Rc = 1/12

stage 1 :  
Ra x 1hour = 1/4 x 1hour = 1/4 = 6/24

stage 2 :  
(Ra + Rb) x 1hour = (1/4 + 1/6) x 1hour = 10/24

stage 3 : 
(Ra + Rb + Rc ) x Time = remaining work

remaining work = 1 - (6/24 + 10/24) = 8/24

So, (1/4 + 1/6 + 1/12) x Time = 8/24
12/24 x Time = 8/24
Time = 2/3 = 40 min

Finally,
Stage 1 + stage 2 + stage 3 = 1h + 1h + 40min = 2h40min
9h + 2h40 = 11h40, answer choice B

Senthil1981 · Answer

I like putting things in a table , that helps to proceed without making a mistake.

A , B and C can do 1/4, 1/6 and 1/12 each individually and respectively.

so 
Time___Person involved_____Word done_________Remaining
9:00_______A________________0________________1
10:00____A (B just joins)_______1/4_______________3/4
11:00__A,B,(C just joins)__1/4 + (1/4 +1/6) = 2/3__1 - (1/4 + (1/4 +1/6)) = 1/3

So 1/3 is done by A+B+C, who can do 1/4+1/6+1/12 = 1/2 in an hour, so would need, 2/3 hour for remaining, which is 2/3* 60min = 40 mins.
Therefore 11:40.
(Excuse me for my formatting.)

gracie · Answer

let t=total time
1/4+5/12+(t-2)(1/2)=1
t=2 2/3 hrs=2 hrs 40 min
9 am+2 hrs 40 min=11:40 am

JeffTargetTestPrep · Answer

We are given that A, B, and C, working alone, finish constructing a house in 4, 6, and 12 hours respectively.
 
Thus, we can let the rate of A = 1/4, the rate of B = 1/6, and the rate of C = 1/12.
 
We can let x = the number of hours the three people work together when C joins in.
 
Thus, the number of hours A works is 2 + x, the number of hours B works is 1 + x, and the number of hours C works is x.
 
We can now determine x with the following equation:
 
work of A + work of B + work of C = 1
 
(2 + x)/4 + (1 + x)/6 + x/12 = 1
 
Multiplying the entire equation by 12, we have:
 
3(2 + x) + 2(1 + x) + x = 12
 
6 + 3x + 2 + 2x + x = 12
 
6x = 4
 
x = 4/6 = 2/3 hour = 40 minutes
 
Since A started at 9 a.m., they finished constructing the house 2 hours and 40 minutes later, or 11:40 a.m.
 
Answer: B

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