alice can do a work in 20 days and bob in 15 days. if they work on it together for 4 days, then what fraction of the job is left?
alice can do a work in 20 days and bob in 15 days. if they work on it together for 4 days, then what fraction of the job is left?
Answer:
Let’s assume that the total work to be done is equal to 1 unit.
Alice can do the work in 20 days, which means her daily work rate is:
1/20
Bob can do the work in 15 days, which means his daily work rate is:
1/15
When they work together, their combined daily work rate is:
1/20 + 1/15 = 3/60 + 4/60 = 7/60
This means that they can complete 7/60th of the work in a day when working together.
If they work together for 4 days, then the work done by them is:
Work done = (Combined work rate) x (Time taken)
Work done = (7/60) x 4
Work done = 7/15
This means that they have completed 7/15th of the total work in 4 days. Therefore, the fraction of the job left is:
Fraction of job left = 1 - Work done
Fraction of job left = 1 - 7/15
Fraction of job left = 8/15
Hence, the fraction of the job left after 4 days of working together is 8/15.