Question

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.

Answer 1

18 minutes

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 =
`(12)/(1000)((S)/(E) )`

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

`T=(12)/(1000) ((36000)/(24) )=18\\`

T = 18 minutes