Question

As the summer heats up, everyone loves going to the California Dreamin' Water Park - primarily because of their most popular ride, a series of water slides called Grizzly Mountain. When the park opens each day at 10 a.m., guests enter the park and rush over to Grizzly Mountain at a constant rate of 11 per minute until 4 p.m. From 4 p.m. until the park closes at 10 p.m. guests arrive at Grizzly Mountain at a constant rate of 4 per minute. The line gets long quickly at Grizzly Mountain so the park built a canopy over the line area that accommodates up to 480 guests waiting in line. Once the line exceeds 480 people, the remaining guests are left to wait in the sun and jump around on the hot sidewalk. The ride operators at Grizzly Mountain send guests down the slides at a constant rate of 430 per hour. Grizzly Mountain begins each day with completely empty lines. What is the maximum number of guests jumping around on the hot sidewalk outside of the Grizzly Mountain canopy on any given day at California Dreamin' Water Park?

Answer 1

4920 people

Step-by-step explanation:

Three things to note:

California Dreamin' Water Park opens by 10 am

The park gets reduced customers from 4pm

The park closes by 10pm

From the above we derive that: Grizzly mountain operates for 12 hours in a day.

From 10am to 4pm, customers enter at 11 people per minute= 11*60=660p/hr=3960 people from 10am to 4pm

From 4pm to 10pm, customers enter at 4 people per minute=

4*60=240p/hr=1440 people from 4pm to 10pm

Grizzly mountain only takes 480 people per hr and so the first 480 people will move in immediately as they enter grizzly with no need to wait at the canopy.

The maximum number of people waiting at the park in a day=3960+1440=5400 people(total people that come to Grizzly mountain in a day) - 480(the first 480 that arrive grizzly mountain) = 4920 people