Juan jogs at an average speed of 7 miles per hour, he walks at an average speed of 3.5 miles per hour. He walks and jogs for 7 hours in which duration he covers a total distance of 6 miles.

Let the time he jogs for be x hours; he walks for 7 - x hours. The distance traveled while he jogs is 7*x and the distance traveled while he walks is (7 - x)*3.5.

7x + (7 - x)*3.5 = 6

=> 7x + 24.5 - 3.5x = 6

This gives a negative value of x which is not possible.

* Juan cannot cover a distance of 6 miles in 7 hours* as his speed in this case would be 6/7 miles per hour. But he walks at a speed of 3.5 miles per hour. To travel 6 miles in 7 hours he would have to spend a part of the 6 hours at rest. In that case the time spent walking and the time spent jogging would not have a unique value.

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