George jogged downhill at 6mi/hr and then jogged back up at at 4mi/hr. If the total jogging time was 1.25 hours, how far did he jog in all?
To find the total distance George jogged, we need to calculate the distance he covered while jogging downhill and then jogging back uphill.
Let's assume the distance George jogged downhill is D.
We know that speed = distance / time.
The time it took George to jog downhill is D/6, and the time it took George to jog back uphill is D/4.
The total jogging time is given as 1.25 hours, so we have the equation:
D/6 + D/4 = 1.25
To solve this equation, we'll first get rid of the denominators by multiplying every term on both sides by 12:
12(D/6) + 12(D/4) = 12(1.25)
2D + 3D = 15
5D = 15
D = 15/5
D = 3
Therefore, the distance George jogged downhill is 3 miles.
Since George jogged back uphill the same distance, the total distance he jogged in all is:
3 + 3 = 6 miles.
So, George jogged a total of 6 miles.
To find the distance George jogged in total, we need to find the distance he jogged downhill and uphill separately, and then add them together.
First, let's find the time it took George to jog downhill. We can use the formula: time = distance / speed.
Let "d" be the distance George jogged downhill. The time taken downhill is given by: time_downhill = d / 6.
Next, let's find the time it took George to jog uphill. Again, using the formula: time_uphill = distance / speed.
Since George jogged uphill at 4 mph, the time taken uphill is: time_uphill = d / 4.
According to the problem, the total jogging time was 1.25 hours. So, we have the equation: time_downhill + time_uphill = 1.25.
Substituting the values we found earlier, we get: (d / 6) + (d / 4) = 1.25.
To solve this equation, let's find a common denominator and combine the terms: (2d + 3d) / 12 = 1.25.
Simplifying, we have: 5d / 12 = 1.25.
Multiply both sides of the equation by 12 to isolate "d": 5d = 15.
Now, divide both sides of the equation by 5: d = 3.
Therefore, George jogged 3 miles downhill and 3 miles uphill.
To find the total distance jogged in all, we add the distance jogged downhill and uphill: 3 miles + 3 miles = 6 miles.
So, George jogged a total of 6 miles.