Carrie can inspect a case of watches in 5 hours. James can inspect the same case of watches in 3 hours. After working alone for 1 hour, Carries stops for lunch. After taking a 40 minute lunch break, Carrie and James work together to inspect the remaining watches. How long do Carrie and James work together to complete the job?
Carrie = 1 case / 5 hours = .2 case/hr
James = 1 case/3 hours = .333 case/hr
together they do .533 case/hr
so
.2 * 1 hr + .533 * x hr = 1 case
.533 x = .8
x = 1.5 hours more
First, let's calculate the work rate of each person.
Carrie can inspect the case of watches in 5 hours, so her work rate is 1/5 of the case per hour.
James can inspect the case of watches in 3 hours, so his work rate is 1/3 of the case per hour.
After working alone for 1 hour, Carrie has inspected 1/5 of the case.
That means there is 4/5 of the case remaining.
Carrie stops for lunch for 40 minutes, which is 40/60 = 2/3 of an hour.
When Carrie and James work together, their combined work rate is the sum of their individual work rates.
So, their combined work rate is 1/5 + 1/3 = 3/15 + 5/15 = 8/15 of the case per hour.
Let's assume that Carrie and James work together for t hours to complete the remaining 4/5 of the case.
Based on their combined work rate, the equation can be set up as:
(8/15) * t = 4/5
To solve for t, let's cross-multiply:
8t = (4/5) * 15
8t = 12
t = 12/8
t = 3/2 = 1.5 hours
Therefore, Carrie and James work together for 1.5 hours to complete the job.
To find out how long Carrie and James work together to complete the job, we need to calculate the amount of work they can do individually in one hour.
Carrie can inspect a case of watches in 5 hours, so in one hour she can inspect 1/5th of the case.
James can inspect a case of watches in 3 hours, so in one hour he can inspect 1/3rd of the case.
After working alone for 1 hour, Carrie stops for lunch. This means she has inspected 1/5th of the case.
After Carrie's lunch break, which is 40 minutes long, she and James work together to inspect the remaining watches. Let's calculate the remaining time they work together.
Since the total time for Carrie's lunch break is 40 minutes, this is equivalent to 40/60 = 2/3 of an hour.
If Carrie worked alone for 1 hour and has already completed 1/5th of the case, then the remaining fraction of the case is 4/5.
When Carrie and James work together, they can inspect a fraction of the case equal to their combined rates. Their combined rate is 1/5 + 1/3 = 3/15 + 5/15 = 8/15 of a case per hour.
To find out how long they need to work together to complete 4/5 of the case, we set up the equation:
(8/15) * x = 4/5
To solve for x, we multiply both sides by 15/8 to isolate x:
x = (4/5) * (15/8)
x = 60/40
x = 1.5
Therefore, Carrie and James need to work together for 1.5 hours to complete the remaining watches.