Respuesta :
The speed of the army up the hill and the distance travelled by the army
up the hill determines the time the army takes to reach the top.
Response:
- The time it takes the army to reach the to of the hill is 6 hours
Which method is used for the finding the time to travel up the hill?
Given:
Distance of the climb = 6 km
Distance of the descent = 4 km
Speed of the army downhill = 2 × The speed uphill
Duration of the journey = 8 hours
Required:
The time it takes the army to reach the top.
Solution:
Let v represent the speed of the army on the way up, we have;
The speed downhill = 2·v
Distance, d= Speed, v × Time, t
[tex]t = \mathbf{\dfrac{d}{v}}[/tex]
Which gives;
[tex]Time \ to \ the \ top, \ t_1 =\mathbf{\dfrac{6}{v}}[/tex]
[tex]Time \ downhill, \ t_2 = \mathbf{\dfrac{4}{2 \cdot v}}[/tex]
- t₁ + t₂ = 8
Which gives;
[tex]\mathbf{\dfrac{6}{v} + \dfrac{4}{2 \cdot v}} = 8[/tex]
[tex]\dfrac{6 \times 2 + 4}{2 \cdot v} =\dfrac{16}{2 \cdot v} = 8[/tex]
2·v × 8 = 16
[tex]v = \dfrac{16}{16} = 1[/tex]
The speed of the army uphill, v = 1 km/hr
Therefore;
- [tex]Time \ to \ the \ top, \ t_1 =\dfrac{6 \, km}{1 \, km/hr} = \underline{6 \ hour}[/tex]
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