A simple work sharing puzzle

[imhotep]

Lionel & Mary can finish painting a room in 2 hours.
Lionel & Noel can finish the same painting job in 3 hours.
Mary & Noel together is able to finish it in 4 hours.

If all three of them work together how long the job will take?
(Assume that each person works at a constant rate whether working as an individual or with the team)

 

[Johnnie_Walker]

Wait

 

[MrFrog]

24/13

 

[kinkon]

Bump

 

[hodakolla]

BUMPER

 

[Solo Rider]

12/7 ??

 

[aruna1]

4 hours

 

[imhotep]

The correct answer is 24/13 as mentioned by @MrFrog

Just think along these lines....

Lionel & Mary ---> in one hour ----> completes 1/2 the job
Lionel & Noel ---> in one hour ----> completes 1/3 the job
Mary & Noel ---> in one hour ----> completes 1/4 the job

 

[aruna1]

The correct answer is 24/13 as mentioned by @MrFrog

Just think along these lines....

Lionel & Mary ---> in one hour ----> completes 1/2 the job
Lionel & Noel ---> in one hour ----> completes 1/3 the job
Mary & Noel ---> in one hour ----> completes 1/4 the job

I disagree.
Process is faster as the slowest sub process in a chain

 

[imhotep]

I disagree.
Process is faster as the slowest sub process in a chain

OK... Lionel & Mary can finish the job in 2 hours. So obviously Lionel, Mary & Noel together has to finish the job less than 2 hours.
24/13 is just less than 2 hours - it's about 1 hr 50 mins.

 

[MrFrog]

The correct answer is 24/13 as mentioned by @MrFrog

Just think along these lines....

Lionel & Mary ---> in one hour ----> completes 1/2 the job
Lionel & Noel ---> in one hour ----> completes 1/3 the job
Mary & Noel ---> in one hour ----> completes 1/4 the job

thanks for the simple but nice puzzle. I did this in the same manner, but using x,y,z for the names . without solving for x or y or z individually, just got the answer for 1 / (x+y+z).

for the guys who didn't do this..
x= no. of rooms Lionel completes in one hour,
y = no. of rooms Mary completes in one hour
z = no. of rooms Noel completes in one hour

x + y = 1/2 ------ (1)
x + z = 1/3 ------ (2)
y + z = 1/4 ------ (3)

(1) + (2) +(3)
x + y + x + z + y + z = 1/2 + 1/3+ 1/4
2 (x + y + z) = 13 / 12
x + y + z = 13 / 24

1 / (x + y + z) = 24 /13

1/ (x+ y + z) This is the answer we need. You should be able to interpret this if you didn't skip the o/l maths lessons

 

[aruna1]

OK... Lionel & Mary can finish the job in 2 hours. So obviously Lionel, Mary & Noel together has to finish the job less than 2 hours.
24/13 is just less than 2 hours - it's about 1 hr 50 mins.

Ya you are correct. I assumed that the section assigned for each person is always the same, which leads to 4 hours