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B) The time, T (in minutes) taken for a stadium to empty varies directly as the number of spectators, S. And inversely as the number of open exits, E.It takes 12 minutes for a stadium to empty when there are 20,000 spectators and 20 open exits. How long does it take the stadium to empty when there are 36.000 spectators and 24 open exits.

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raphealnwobi

Answer:

18 minutes

Step-by-step explanation:

Given that the time (T) varies directly as the number of spectators (S) and varies inversely as number of open exits (E).

Hence:

T ∝ S; T ∝ 1 / E

Let k be the constant of proportionality. This gives:

T = kS / E

when T = 12 minutes, S = 20000, E = 20. Hence:

12 = k(20000) / 20

20000k = 240

k = 12 / 1000

This gives:

T = [tex]\frac{12}{1000}(\frac{S}{E} )[/tex]

When  S = 36000, E = 24, we are to calculate the time (T):

[tex]T=\frac{12}{1000} (\frac{36000}{24} )=18\\[/tex]

T = 18 minutes

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