Fred completes a project in 6 days. Jack can do it in 5 days and David takes only 4 days. How many days would it take to complete if they work together?
Fred can complete a project in 6 days. He completes `1/6` of the project per day. Jack can complete the project in 5 days. He completes `1/5` of the project every day. David can complete the project in 4 days. He completes `1/4` of the project every day.
If the three work together they can complete `1/5 + 1/6 + 1/4 = 37/60` of the project in a day. The time taken by them to complete the project is `60/37` = 1.62 days.
The time taken to complete the project if all the three work together is 1.62 days.
Fred completes the project in 6 days. In 1 day he will complete 1/6 of the project.
Jack completes the same project in 5 days. In 1 day he will complete 1/5 of the project.
David completes the same project in 4 days. In 1 day he will complete 1/4 of the project.
In 1 day all 3 together (Fred, Jack and David) will finish (1/6+ 1/5+ 1/4) of the project.
1/6+ 1/5+ 1/4 = (10+12+15)/60 = 37/60.
since, Fred,Jaclk and David together finishes 37/60 of the project in 1 day
Therefore all 3 togetheher will fonish 1 project in 60/37 days.
60/37 days = 1.62 days
The project will be completed in 1.62 days,if they work together <---Answer
We can find out the part of the project by each in one day and then the part of it completed by all three in one day. From this information we can get the total time required by all three combined as under:
The part of project completed by Fred in one day = 1/6
The part of project completed by Jack in one day = 1/5
The part of project completed by David in one day = 1/4
The part completed by all three combined in one day = 1/6+1/5+1/4
=> (10+12+15)/60 = 37/60
Time required to complete the project by all three = 1/(37/60)
=> = 60/37 = 1.62 days
The project will be completed in 1.62 days if they work together