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A group of $10$ students are on a field trip when their bus breaks down $40$ miles away from the school. A teacher takes $5$ of them back to school in her car, travelling at an average speed of $40$ miles per hour.
The other $5$ students start walking towards school at a steady $4$ miles per hour.
The teacher drops the $5$ at school, then immediately turns around and comes back for the others, again travelling at a steady speed of $40$ miles per hour. How far have the students walked by the time the car reaches them?