John 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 would think
first find the average of her running speed
= 4 m/hr + 6 m/hr = 10 m/hr divided by 2 = an average of 5 m/hr
now 5 m/hr = 1.25 hr
1.25 hr x 5 m/hr = 6.25 miles
Hope that helps, the questions seems a little vague so that's why finding an average of her running speed seems to be the appropriate response.
equate the two distances. distance = speed * time
6t = 4(1.25-t)
6t = 5 - 4t
10t = 5
t = .5
6*.5 = 3
4*.75 = 3
total distance = 6
To find the distance John jogged in total, we need to calculate the distance he jogged downhill and uphill separately, and then add them together.
Let's start with the downhill jog. We know that the speed of the jog downhill is 6 miles per hour. The formula to calculate distance is distance = speed x time. In this case, distance_downhill = 6 miles/hour x time_downhill.
To find time_downhill, we can use the formula time = distance / speed. In this case, time_downhill = distance_downhill / 6 miles/hour.
Next, let's calculate the uphill jog. The speed of the jog uphill is 4 miles per hour. Similarly, distance_uphill = 4 miles/hour x time_uphill.
To find time_uphill, we can use the same formula: time_uphill = distance_uphill / 4 miles/hour.
Now, we are given that the total jogging time was 1.25 hours. This means that the sum of time_downhill and time_uphill is equal to 1.25 hours: time_downhill + time_uphill = 1.25.
We can substitute the formulas for time_downhill and time_uphill into the equation above and solve for distance_downhill and distance_uphill:
(distance_downhill / 6) + (distance_uphill / 4) = 1.25
Now, we have one equation with two unknowns. However, we can use another given piece of information: the total distance jogged is equal to the sum of distance_downhill and distance_uphill.
So, distance_downhill + distance_uphill = total distance jogged.
We can rewrite this equation as: distance_downhill + distance_uphill = total distance
Substituting the values obtained above for distance_downhill and distance_uphill, the equation becomes:
(distance_downhill / 6) + (distance_uphill / 4) = 1.25
Now we have two equations:
(distance_downhill / 6) + (distance_uphill / 4) = 1.25
distance_downhill + distance_uphill = total distance
We can solve these simultaneous equations using substitution or elimination method to find the values of distance_downhill and distance_uphill.
Once we have the values of distance_downhill and distance_uphill, we can calculate the total distance jogged by adding them together:
total distance = distance_downhill + distance_uphill
This will give us the answer to the question: How far did John jog in total?