I am reposting the question below because none of the answers I received are correct/possible. The TOTAL has to be six miles in seven hours.
Juan jogs a certain distance and then walks a certain distance. When he jogs he averages seven miles per hour. When he walks, he averages 3.5 miles per hour. If he walks and jogs a total of six miles in a total of seven hours, how far does he jog and how far does he walk?
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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.
We should say that the problem has a numerical answer that satisfies the given conditions, but it can only happen in the Twilight Zone.
Maybe this works.
let Juan walk for 5 hours or 17.5 miles.
Let Juan jog for 2 hours or 14 miles.
If the angle between walking and jogging is 0.312621419 radians, then the resulting displacement will be 6 miles by the law of cosines.
36 = 17.5^2 +14^2 - 2*17.5*14*cos(0.312621419 radians)
or the angle would be about 17.9 degrees.
The average speed during 6 hours Walk & Jog = 6/7 miles/hour
This speed is less than both the speeds i.e. Walk (7 miles/hour) and Jog (3.5 miles/hour). In this case the 7 hours target for 6 miles can be achieved only and only if:
1. One of the Walk/Jog average speed is less than 6/7 miles/hour and the other is more than 6/7 miles per hour
2. Both the average speeds for walk and jog are equal to 6/7 miles/hour
If both the average speeds are more than 6/7 miles per hour than there must be a rest period to make up the total time of 6 hours.
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