Jeff hiked for 2 hours and traveled 5 miles. If he continues at the same pace, which equation will show the relationship between the time \( t \) (in hours) he hikes to the distance \( d \) (in miles)? Will the graph be continuous or discrete?

A. \( d = 0.4t \), discrete
B. \( d = 0.4t \), continuous
C. \( d = 2.5t \), discrete
D. \( d = 2.5t \), continuous

Answer:d = 2.5t, continuous ;

Answered by gpacheco12345678911 | 2024-06-12

Jeff is traveling at the same pace, so he is moving at constant speed: its motion is a uniform motion, so the distance he covers (d) as a function of the time (t) is expressed by the law
d = v t (1)
where v is Jeff's speed.
We can find the speed from the initial data:
t = 2 hours
d = 5 miles
so, the speed is given by the ratio between the distance and the time
v = t d ​ = 2 h 5 mi l es ​ = 2.5 m p h
Therefore, equation (1) becomes
d = 2.5 t
and the graph is continuous, because t can have any real value.

Answered by skyluke89 | 2024-06-25

The equation that shows the relationship between the time Jeff hikes and the distance he travels is d = 2.5 t . The graph will be continuous because time can take any real value. Therefore, the correct answer is D: d = 2.5 t , continuous.
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Answered by skyluke89 | 2024-08-09