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Travel on a river problem
By Isabelle Soh (P2842) on Wednesday, August 30, 2000 - 10:19 am:

Hi everybody!!! My name is Isabelle, I'm 10 and am in Year 7 in Australia. I'm in a gifted and talented maths class at school. We were given this very hard problem and we're supposed to try to find a formula and answer. THE MIND BOGGLES!!

The problem is - Tom was floating down the river on a raft when, 1 km lower down, Michael took to the water in a rowing boat. Michael rowed downstream at the best pace of which he was capable. Then he turned around and rowed back again and arrived at his starting point just as Tom drifted by. If Michael's rowing speed in still water is ten times the speed of the current in the river, what distance had Michael covered before he turned his boat around.

Please help me - thanks!!!!

ISABELLE

By Andrew Smith (P2517) on Wednesday, August 30, 2000 - 10:38 pm:

Suppose the speed of the current is c, and the distance Michael covers before turning round is D.

Michael travels downstream distance D at a speed of 11c and thus takes time D/(11c)
Upstream, distance D is covered at a speed of 9c and thus takes time D/(9c)
This gives a total time of (1/11 + 1/9)*D/(c).

Also Tom travels at speed c and covers 1km so
d = s×t
1 = c×(1/11 + 1/9)×D/(c)
= (1/11 + 1/9)×D
Giving D = 4.95km.