A carousel at Playland, contains 38 horses. each carousel ride takes 4 minutes, riders need 3 minutes to exit and newcomber require 3 minutes to pick a horse and hop on. A carousel ride costs $0.75. The carousel makes $88,239.00 a year. How many horses are occupied per ride, on average, if the carousel is open from 11am to 5:30pm every day of the year? (assume that this is not a leap year.)

arggh, just a lot of arithmetic.....

time per day open for rides:
6.5 hours
= 390 minutes
time available per year
= 390(365) = 142350 minutes

time needed to complete one ride
= 3 + 4 + 3 = 10 minutes.
(so they can complete 39 rides per day)

number of rides per year = 142350/10 = 14235
(notice 39x365 = 14235)

revenue per ride = 88239/14235 = $ 6.199
number of horses used per ride = 6.199/.75
= 8.26 horses

or

revenue per day= 88239/365 = $ 241.75

rides per day = 39 (see above)
revenue per ride = 241.75/39 =$ 6.199
number of riders per ride or
number of horses used = 6.199/.75 = 8.26 horses

To find the average number of horses occupied per ride, we need to calculate the total number of rides in a year and divide it by the total number of horses on the carousel.

First, let's find the total number of minutes the carousel is operational in a year:
The carousel is open from 11 am to 5:30 pm, which is a total of (5:30 pm - 11 am) = 6.5 hours.
Therefore, the total number of minutes the carousel is operational each day is 6.5 hours * 60 minutes/hr = 390 minutes.

Next, let's find the number of rides the carousel can complete in a day:
The time taken per ride is 4 minutes for the ride, 3 minutes for riders to exit, and 3 minutes for newcomers to pick a horse and hop on, totaling 4 + 3 + 3 = 10 minutes per ride.
Therefore, the carousel can complete 390 minutes / 10 minutes per ride = 39 rides per day.

Now, let's find the number of rides in a year:
The carousel is open every day of the year, so the total number of days it is open is 365.
Therefore, the total number of rides in a year is 39 rides per day * 365 days = 14,235 rides.

Finally, let's find the average number of horses occupied per ride:
The total amount earned in a year is $88,239.00, and each ride costs $0.75.
Therefore, the total number of rides in a year is $88,239.00 / $0.75 = 117,652 rides.

To find the average number of horses occupied per ride, we divide the total number of horses on the carousel by the total number of rides:
Average number of horses occupied per ride = Total number of horses / Total number of rides
Average number of horses occupied per ride = 38 horses / 14,235 rides ≈ 0.0027 horses per ride.

Therefore, on average, approximately 0.0027 (or about 0.27%) of the horses on the carousel are occupied per ride.