Answer:
3.5 days
Step-by-step explanation:
You want to know the number of days until work is completed if P works every day and Q and R work on alternate days, given P, Q, R can finish the work individually in 5, 10, and 15 days, respectively.
When each works alone, the amount of work completed in one day is ...
P: 1/5
Q: 1/10
R: 1/15
On odd days, when P and Q work together, the amount of work completed is ...
(1/5) +(1/10) = 3/10
On even days, when P and R work together, the amount of work completed is ...
(1/5) +(1/15) = 4/15
Both of these values are less than 1/3, so we know it will take at least 3 days to complete the work. In 3 days, the work completed is ...
3/10 + 4/15 + 3/10 = 13/15 . . . . . . . . of the job
So, after 3 days, the amount of work remaining is ...
1 -13/15 = 2/15
On the 4th day, the work is completed at the rate of 4/15 job per day, so the fraction of the day required to finish up is ...
[tex]\dfrac{\text{remaining work}}{\text{work per day}}=\dfrac{2/15}{4/15}\text{ day}=\dfrac{2}{4}\text{ day}=\dfrac{1}{2}\text{ day}[/tex]
The work can be completed in 3 1/2 days using the given schedule.
