Algebra:Quadratic Equation

羅庚

2010-01-21 3:27 am

Two turnstiles A and B admit to a football ground. On an average it takes a spectator 0.2 second longer to pass through A than through B, and B admits on an average 10 more spectators per minute than A. How many spectators can enter the ground in a quarter of an hour?

回答 (1)

用戶9112

2010-01-21 3:42 am

✔ 最佳答案

Let the time for a spectator to pass through A be x sec.
Then the time for a spectator to pass through B is (x – 0.2) sec
Spectator admission per minute for A and B are 60/x and 60/(x – 0.2) respectively
Hence 60/(x – 0.2) – 60/x = 10
60x – 60(x – 0.2) = 10x(x – 0.2)
12 = 10x^2 – 2x
5x^2 – x – 6 = 0
(5x - 6)(x + 1) = 0
x = 1.2 or x = -1 (rejected)
Therefore total spectator admitted per minute is 60/1.2 + 60/(1.2 – 0.2)
= 50 + 60 = 110Spectator admission in a quarter of an hour = 110 * 60/4 = 1650

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