About ratio........HOMEWORK

400/a : 400/b : 400/c
= 1/a : 1/b : 1/c

Let the time taken by A is a*k where k is a constant.
Then the time taken by B is b*k and by C is c*k
Speed of A = 400 / (ak)
Speed of B = 400 / (bk)
Speed of C = 400 / (ck)
Speed of A : Speed of B = (400 / (ak)) / (400 / (bk))
= b : a
Speed of B : Speed of C = (400 / (bk)) / (400 / (ck))
= c : b

Multiply (Speed of A : Speed of B) by c
=> Speed of A : Speed of B = bc : ca

Multiply (Speed of B : Speed of C) by a
=> Speed of B : Speed of C = ca : ab

Hence Speed of A : Speed of B : Speed of C = bc : ca : ab

2006-12-06 01:07:34 補充：
It is a common mistake that simply take 400/a to be the speed of A, 400/b to be that of B and 400/c to be that of C and then derive their speed ratio. a:b:c only represent the ratio of their time taken.

2006-12-06 01:08:12 補充：
e.g., if a:b:c = 1:2:3, it does NOT mean A takes 1s, B takes 2s and C takes 3s. They can be 4s, 8s &12s, and so on. So their speed cannot be simply 400/a, 400/b and 400/c. A common method is to insert a multiplier k, then derive their speeds in terms of k and finally get the required ratio.

Since, spped = distance / time (ms-1)
Ratio of the running speeds = 400/a : 400/b : 400/c = 1/a : 1/b : 1/c