Respuesta :
Let the total length of Ted's hike be L and the total time spent be T.
The time spent going down is t, and the time spent going up is t+40 (if t is measured in minutes) or t + 2 hr/3 (if t is measured in hours). Note that t + t + 2/3 must equal T, the total hiking time, with all measurerments in hours.
Distance uphill: L = (3 mph)(t+2/3) = Distance downhill: (5 mph)(t)
We need only find t, the am't of time req'd for Ted to go up to down.
3t + 2 = 5t, or 2 = 2t, or t = 1 (hour)
It will take Ted 1 hour to descend the hill and 1 2/3 hour to ascend the hill.
The total length of Ted's hike was then 2 2/3 hours, or 2 hours 40 minutes.
By the way, the distance in each direction is (5 mph)(1 hr) = 5 miles.
The time spent going down is t, and the time spent going up is t+40 (if t is measured in minutes) or t + 2 hr/3 (if t is measured in hours). Note that t + t + 2/3 must equal T, the total hiking time, with all measurerments in hours.
Distance uphill: L = (3 mph)(t+2/3) = Distance downhill: (5 mph)(t)
We need only find t, the am't of time req'd for Ted to go up to down.
3t + 2 = 5t, or 2 = 2t, or t = 1 (hour)
It will take Ted 1 hour to descend the hill and 1 2/3 hour to ascend the hill.
The total length of Ted's hike was then 2 2/3 hours, or 2 hours 40 minutes.
By the way, the distance in each direction is (5 mph)(1 hr) = 5 miles.
Answer:
The total distance used by Ted was 10 miles, uphill and downhill.
Step-by-step explanation:
Givens:
- Uphill hike: [tex]s=3\frac{mi}{hr}[/tex]; [tex](t+40)min[/tex]
- Downhill: [tex]s=5\frac{mi}{hr}[/tex]; [tex]t min[/tex]
So, Ted climbs the same distance in both directions, because it's the same trajectory, but at different speeds:
[tex]d_{uphill}=d_{downhill}[/tex]
Applying the definition of a constant movement: [tex]d=st[/tex], we have:
[tex]3\frac{mi}{hr}(t+40)min=5\frac{mi}{hr}t min[/tex]
However, we first need to transform the time in hours, because the speed is using hours in its unit. So, we know that 1 hour equals 60 minutes:
[tex]40min\frac{1hr}{60min}=0.67 hr[/tex]
Therefore, the equation will be:
[tex]3\frac{mi}{hr}(t+0.67)hr=5\frac{mi}{hr}(t \ hr)\\3t+2=5t\\2=5t-3t\\2=2t\\t=\frac{2}{2}=1 \ hr[/tex]
Therefore, downhill we took 1 hour, and uphill he took 1.67 hr or 1 hr and 40 min.
Now, we use this time to find the length of Ted's hike.
Uphill:
[tex]d_{uphill}=3\frac{mi}{hr}1.67 hr \\d_{uphill}=5mi[/tex]
Downhill:
[tex]d_{downhill}=5\frac{mi}{hr}1 hr \\d_{uphill}=5mi[/tex]
Therefore, the total distance used by Ted was 10 miles, uphill and downhill.
