Respuesta :
Answer:
[tex]v_{avg} = 49.5 mph[/tex]
Explanation:
Let the distance moved by Joe is "d"
so the time taken by him to drove it by speed 45 mph is given as
[tex]t_1 = \frac{d}{v_1}[/tex]
[tex]t_1 = \frac{d}{45}[/tex]
now the same distance is traveled by him with speed 55 mph
so the time taken by him
[tex]t_2 = \frac{d}{55}[/tex]
so total time taken by him for complete distance 2d
[tex]t = t_1 + t_2[/tex]
[tex]t = \frac{d}{45} + \frac{d}{55}[/tex]
[tex]t = 0.0404 d[/tex]
now the average speed is given as
[tex]v_{avg} = \frac{2d}{t}[/tex]
[tex]v_{avg} = \frac{2d}{0.0404d}[/tex]
[tex]v_{avg} = 49.5 mph[/tex]
Answer:
47.37 miles per hour,
Explanation:
The average speed is given by the formula
Average speed =(total distance / total time)
Let the distance Joe traveled at a speed of 45 miles per hour be 'D', because he then drove the same distance with a speed of 50 miles per hour then, the total distance is '2D'.
The total time will be the time he drove at a speed of 45 miles per hour ([tex]t_{1}[/tex]) plus the time he drove at a speed of 50 miles per hour ([tex]t_{2}[/tex]).
Then the average speed is :
[tex]v_{average} = \frac{2D}{t_{1}+t_{2}}[/tex].
Because we know that uniform rectilinear motion is discribed by the ecuation
[tex]d=\v*t[/tex] (where d is distance, v is a constant speed and, t is the time)
we can express both times in terms of speeds and the distance, thus
[tex]t_{1} =\frac{D}{v_{1}}[/tex] and,
[tex]t_{2} =\frac{D}{v_{2}}[/tex].
So now the average speed [tex]v_{average} = \frac{2D}{t_{1}+t_{2}}[/tex] can be written as follows:
[tex]v_{average} = \frac{2D}{(\frac{D}{v_{1}}+\frac{D}{v_{2}} )}[/tex]
[tex]v_{average} = \frac{2D}{D(\frac{1}{v_{1}}+\frac{1}{v_{2}} )}[/tex]
[tex]v_{average} = \frac{2}{(\frac{1}{v_{1}}+\frac{1}{v_{2}} )}[/tex]
[tex]v_{average} = \frac{2}{(\frac{1}{45}+\frac{1}{50} )}[/tex]
[tex]v_{average} = 47.37[/tex] miles per hour.
