Question

If the egress rate for a stadium is 5,500 fans per hour and it takes fans about one-third less time for fans to exit a game as it does for them to enter and find their seats, what is the ingress rate? (Round up to a whole number.)

Answer 1

The ingress rate is approximately 3,667 fans per hour.

Step-by-step explanation:

The question is asking for the ingress rate, which is the rate at which fans enter the stadium. We are given that the egress rate is 5,500 fans per hour. It also states that it takes fans about one-third less time to exit a game than it does for them to enter and find their seats.

To find the ingress rate, we need to calculate the time it takes for fans to exit a game. If it takes one-third less time to exit than to enter, we can say that it takes two-thirds of the time to exit. Therefore, the egress time is two-thirds of the ingress time.

Let's assume the ingress rate is x fans per hour. The egress rate is 5,500 fans per hour. We can set up the following equation: 5,500 = x / (2/3x). To solve for x, we can multiply both sides of the equation by (2/3x) to eliminate the fraction: 5,500 * (2/3x) = x. Simplifying this equation, we get: 11,000 / 3 = x, or approximately 3,667 fans per hour. Therefore, the ingress rate is approximately 3,667 fans per hour.

Answer 2

`16,500(fans)/(hour)`

Step-by-step explanation:

Givens:

• Egress rate is 5,500 fans per hour.
• Egress rate is one-third than ingress rate. In other words, the ingress rate is 3 times faster than the egress rate. This interpretation is what solves this problem. It's the needed relation to answer the question.

Now, we have to express this in math, to calculate:

`Egress=5,500(fans)/(hour)`

`Egress=(1)/(3)Ingress`

Now, we replace and solve for Ingress:

`5,500(fans)/(hour)=(1)/(3)Ingress\\Ingress=3(5,500(fans)/(hour))\\Ingress=16,500(fans)/(hour)`

Therefore, based on the givens, the ingress rate is
`16,500(fans)/(hour)`