A family of snails takes one hour to cross a lawn, from the time that the first snail puts its 'nose' onto...

arithmetic/snails.crossing New

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Problem

A family of snails takes one hour to cross a lawn, from the time that
the first snail puts its 'nose' onto the lawn until the last drags its
tail completely off.  The snails cross single file in a straight line,
nose to tail (if snails have noses).

The lawn is just wide enough to accommodate two-thirds of the family at
once.  The snails are all identical and travel at the same speed, and
each has its whole body on the lawn for 20 minutes exactly.

How many snails in the family?

-- Gerry Quinn <gerryq@indigo.ie>

Show solution

I define:
        N - the number of snails
        s - the length of a snail
        L - the length of lawn to travers
        d - the total distance to cover

d = L + Ns

There must be an integer, m, such that N = 3m. Then L=2N/3 * s = 2ms.

Now I calculate the velocity of the snails two ways:

v = (L - s)/20min = d/60min

Giving...

        3(L - s)        =        L + Ns
        3(2ms - s)        =        2ms + 3ms
        3(2m-1)s        =        5ms
        6m-3                =        5m
        m                =        3

9 snails.

-- David McKee <dmckee@nmsu.edu>