The Postie's Pace

Camelia, the friendly mail deliverer, takes breaks from her route at the top of every hour. The amount of time Camelia rests is directly proportional to the speed at which she walks after her break.

If Camelia rests for 10 minutes every hour, she is able to walk at the rate of 4 miles/hour.

If Camelia rests for only 5 minutes every hour, she is able to walk at the rate of 3 miles/hour.

Camelia begins her walk at 2:30 p.m. What would be the optimum amount of time for Camelia to rest every hour, if she is to complete her 10-mile delivery route in the fastest possible time? What time does Camelia complete her route?

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