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Emily takes a trip, driving with a constant velocity of 89m5 m/s to the north except for a 22 min rest stop. if Emily's average velocity is 77.8 m/s to the north, how long does the trip take?

Respuesta :

Emily moves with speed 89.5 m/s

let it travel for time "t" so the distance covered by it

[tex]d = v* t[/tex]

[tex]d = 89.5 * t[/tex]

now the average speed is given as

[tex]v_{avg} = \frac{d}{T}[/tex]

here total time of the journey will be given as

[tex]T = 22*60 + t = 1320 + t[/tex]

now we have

[tex]77.8 = \frac{89.5*t}{t + 1320}[/tex]

[tex]102696 + 77.8t = 89.5 t[/tex]

[tex]102696 = 11.7 t[/tex]

[tex]t = 8777.4 s[/tex]

[tex]t = 2.44 h[/tex]

so it will move for t = 2.44 h

so the total time of the trip would be given by adding waiting time or time of stop

[tex]t = 8777.4 + (22*60) [/tex]

[tex]t = 10097.43s[/tex]

[tex]t = 2.80 hr[/tex]

so his total time of journey is 2.8 h

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