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 =
When S = 36000, E = 24, we are to calculate the time (T):
T = 18 minutes
You can try the choices to see which one works. The differences between an values double each time. They have the sequence 1, 2, 4, 8. So, you know that choices A) and D) do not work. They show the difference to be constant at 1 or 8. Since the differences are multiplied by 2, C) is a reasonable choice. Trying that, we find it describes the sequence perfectly:
a2 = 2·2 -1 = 3
a3 = 2·3 -1 = 5
a4 = 2·5 -1 = 9
a5 = 2·9 -1 = 17
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Trying choice B on the last term, we have
... a5 = 3·a4 -3 = 3·9 -3 = <em>24 ≠ 17</em>