James 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?
I just answered a question like this a couple questions below this post!
d = 6 t
d = 4(1.25-t)
we want 2 d
so
6 t = 5 - 4 t
10 t = 5
t = .5
then d = 6 * .5 = 3
so
2d = 6 miles
THANX!!!!!!!
To find how far James jogged in total, we can break the problem into two parts: the time he spent jogging downhill and the time he spent jogging uphill.
Let's start with the time spent jogging downhill. We know that James jogged at a speed of 6 miles per hour. To find the time spent jogging downhill, we can use the formula: time = distance / speed. Let's call the distance he jogged downhill "D".
So, the time spent jogging downhill is D / 6.
Next, let's consider the time spent jogging uphill. We know that James jogged at a speed of 4 miles per hour. Let's call the distance he jogged uphill "U". Using the same formula, the time spent jogging uphill is U / 4.
Since we know that the total jogging time was 1.25 hours, we can set up an equation: D / 6 + U / 4 = 1.25.
Now, we can solve for either D or U by rearranging the equation. Let's solve for D:
D / 6 = 1.25 - U / 4
Multiply both sides of the equation by 6 to eliminate the fraction:
D = 7.5 - 1.5U
Now, we can substitute this expression for D back into the equation to solve for U:
7.5 - 1.5U + U / 4 = 1.25
Multiply both sides of the equation by 4 to eliminate the fraction:
30 - 6U + U = 5
Combine like terms:
30 - 5U = 5
Subtract 30 from both sides:
-5U = -25
Divide both sides by -5:
U = 5
Now that we have the value for U, we can substitute it back into D = 7.5 - 1.5U to find D:
D = 7.5 - 1.5(5)
D = 7.5 - 7.5
D = 0
This means that James did not jog any distance downhill. Therefore, the total distance he jogged is just the distance uphill, which is U = 5 miles. So, James jogged a total of 5 miles in all.