Swimming Laps

Date: 04/15/2002 at 00:40:54
From: Tom
Subject: Maths Problem

Mr. John decides to swim a certain number of laps of the pool in five 
days. On the first day he covers one fifth of the total. The next day 
he swims one third of the remaining laps. On the third day he covers 
half of the remaining laps, and on the fourth day he swims one quarter 
of the remainder. He still has 24 laps to swim.

How many laps has Mr. John swum?

Date: 04/15/2002 at 11:51:10
From: Doctor Ian
Subject: Re: Maths Problem

Hi Tom,

The total number of laps must be 

  total =   (laps on first day) 
          + (laps on second day)
          + (laps on third day)
          + (laps on fourth day)
          + remainder

We're told the remainder:

  total =   (laps on first day) 
          + (laps on second day)
          + (laps on third day)
          + (laps on fourth day)
          + 24

If the total number of laps is L, then the number he swims on the 
first day must be L/5:

      L =   L/5
          + (laps on second day)
          + (laps on third day)
          + (laps on fourth day)
          + 24

If you find expressions for the other days in terms of L, you'll 
end up with something that looks like 

  L = L/5 + ... + 24

which is one equation with one variable. If you solve this equation 
for L, you'll know how many laps he set out to swim. 

Can you take it from here?  Write back if you'd like to talk more
about this, or anything else.

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/