中四數學問題一元二次方程(Eng)

[匿名]

2011-09-24 7:53 pm

1.Tom and Mary are due south and due east of a bus stop respectively,and the distance between them is 60m.They walk towards the bus stop at the same time with their own constant speeds.After 6 seconds,they are both 27m away from the bus stop.If Mary walks slower than Tom by 2m/s,find their speeds.

回答 (1)

用戶2053

2011-09-24 8:38 pm

✔ 最佳答案

1)Let the speed of Mary = M m/s , Tom = T m/s :M + 2 = T .....(1)
The distance between Mary and the bus stop= 6M + 27The distance between Tom and the bus stop= 6T + 27
So (6M + 27)² + (6T + 27)² = 60² ......(2)Sub (1) into (2) :(6M + 27)² + (6(M+2) + 27)² = 60² 9 (2M + 9)² + 9 (2(M+2) + 9)² = 3600(2M + 9)² + (2M + 13)² = 4004M² + 36M + 81 + 4M² + 52M + 169 = 4004M² + 44M - 75 = 0(2M - 3) (2M + 25) = 0M = 3/2 or M = - 25/2 (rejected)T = 3/2 + 2 = 7/2
Tom speed = 7/2 = 3.5 m/s
Mary speed = 3/2 = 1.5 m/s

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