time_format.ex

defmodule TimeFormat do
  def format(seconds) do
    hours = div(seconds, 3600)
    remainder = rem(seconds, 3600)
    minutes = div(remainder, 60)
    seconds = rem(remainder, 60)
    format(hours, minutes, seconds)
  end

  defp format(0, minutes, seconds), do: "#{minutes}:#{pad(seconds)}"
  defp format(hours, minutes, seconds), do: "#{hours}:#{pad(minutes)}:#{pad(seconds)}"

  defp pad(number), do: :io_lib.format('~2..0B', [number])
end

time_format_test.exs

defmodule TimeFormatTest do
  use ExUnit.Case
  import TimeFormat

  test "format/1 conforms to the spec" do
    assert "0:00" == format(0)
    assert "0:57" == format(57)
    assert "0:59" == format(59)

    assert "1:59" == format(119)
    assert "22:01" == format(22 * 60 + 1)
    assert "59:00" == format(59 * 60)
    assert "59:09" == format(59 * 60 + 9)
    assert "59:59" == format(59 * 60 + 59)
    assert "1:00:00" == format(3600)

    assert "1:00:01" == format(3601)
    assert "1:01:00" == format(3660)
    assert "1:01:01" == format(3661)
    assert "1:12:21" == format(3600 + 12 * 60 + 21)
    assert "2:12:21" == format(2 * 3600 + 12 * 60 + 21)
    assert "12:12:21" == format(12 * 3600 + 12 * 60 + 21)

    assert "0:07" == format(7)
    assert "0:30" == format(30)
    assert "1:00" == format(60)
    assert "12:12" == format(12 * 60 + 12)
    assert "1:23:04" == format(3600 + 23 * 60 + 4)
  end
end