數學題目疑問2

Let speed of Hung be x,
speed of Ming be y.
Distance between the 2 places = 90 km,
so time taken by Ming = 90/y.
time taken by Hung = 90/x.
Therefore, 90/y = 90/x + 3/60........(1)
Time taken by Ming for the 1st 30 km = 30/y.
Time taken by Ming for the remaining 60 km at speed y + 10 = 60/(y + 10).
Therefore, 30/y + 60/(y + 10) = 90/x....................(2)
From (1) and (2) we get
30/y + 60/(y + 10) = 90/y - 3/60
60/(y + 10) = (90 - 30)/y - 1/12
= 60/y - 1/12
720y = 720(y + 10) - y(y + 10)
720y = 720y + 7200 - y^2 - 10
y^2 + 10 - 7200 = 0
(y + 90)(y - 80) = 0
y = - 90 (rej.) or 80 km/h = speed of Ming.
Sub. into (1)
90/80 = 90/x + 1/12
9/8 - 1/12 = 90/x
25/24 = 90/x
x = 86.4 km/h = speed of Hung.
Time taken for the whole journey = 90/86.4 x 60 = 62.5 min.
Time taken by Ming to travel 30 km = 30/80 = 3/8 hr.
Distance travelled by Hung in 3/8 hr. = 86.4 x 3/8 = 32.4 km.
so distance between them = 32.4 - 30 = 2.4 km.







2009-07-09 07:35:35 補充：
To : 002
Thank you for the translation since Iverson asked for it. Thanks.

x=國雄的速度
y=澤明的速度
九龍到東涌的距離=90km
國雄用左既時間=90/y
澤明用左既時間=90/x
所以90/y = 90/x + 3/60------(1)
頭30km 澤明用左既時間 = 30/y
餘下60km,澤明剩低既時間以 速度y + 10 = 60/(y + 10).
所以30/y + 60/(y + 10) = 90/x
由 (1) 同(2) 我地 得到
30/y + 60/(y + 10) = 90/y - 3/60
60/(y + 10),= (90 - 30)/y - 1/12
= 60/y - 1/12
720y = 720(y + 10) - y(y + 10)
720y = 720y + 7200 - y^2 - 10
y^2 + 10 - 7200 = 0
(y + 90)(y - 80) = 0
y = - 90 (rej.) or 80 km/h = 澤明的速度
sub.(2) into (1)
90/80 = 90/x + 1/12
9/8 - 1/12 = 90/x
25/24 = 90/x
x = 86.4 km/h = 國雄的速度
整個旅程既時間= 90/86.4 x 60 = 62.5 分鐘
澤明行30km既時間 = 30/80 = 3/8 小時
國雄行左既距離in 3/8小時. = 86.4 x 3/8 = 32.4公里
國雄同澤明相差既距離 = 32.4 - 30 = 2.4 公里

譯左上面人兄既答案,希望你唔好介意