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Luke and Slim have only one horse between them. Luke rides a certain time and then ties up the horse for Slim, who has been walking. Meanwhile Luke walks on ahead. They proceed in this way, alternately walking and riding. If they walk 4 miles per hour and ride 12 miles per hour, what part of the time is the horse resting?

1 answer

Consider the 1st hour
Luke goes 12 miles while Luke goes 4
Luke then has to walk 2 more hours to get to the horse.
Now Luke is still 8 miles ahead, and during the next hour, Slim rides 12 miles while Luke walks another 4 miles, and they meet again.
By this time 4 hours have passed, and the horse has rested 2 hours.
so, ...
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