Word Problem

[deichgraf]

3 machines can do a particular work in 4hr, 6hr, and 8hr respectively. If all machines work together simultaneously for doing the same work, what will be the contribution of the fastest machine (in hrs) ?

[Abhishek009]

3 machines can do a particular work in 4hr, 6hr, and 8hr respectively. If all machines work together simultaneously for doing the same work, what will be the contribution of the fastest machine (in hrs) ?

Let the total work be 24 units .

Now efficiency of the first machine is 6 units/hr

Efficiency of the second machine is 4 units/hr

Hence contribution of the first worker is 6/24 = 1/4

[n_sun30]

ans will be 24/13 if the finding is the work done together by the three machines. but what is the contribution of the first machine?

[tractable]

All machines need to work simultaneously for 24/13 hours, even the fastest has to work for 24/13 hrs.
The contribution of work for each machine is different, here the fastest machine contribution = (24/13)*1/4=6/13 ~ 46.1 %

[saint4life]

Total time taken by the three machines is 24/13.
Since the fastest one is the one that takes least time and it does 1/4th of the work, answer is 6/13.

[orchidthief88]

yes, saint4life has the correct answer.

if we add the rates of work, 1/4 + 1/6+ 1/8 = the combined rate of work = 13/24

thus it will take 24/13 hours to complete one unit of work. This makes sense, it will take about 2 hours or so for the work to be completed when all 3 machines are working. Of that amount of time, the fastest machine accounts for 1/4. So 1/4*24/13 = 6/13 hours.