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A person takes a trip, driving with a constant speed of 89.5km/h, except for a 22min rest stop. If the person's average speed is 77,8km/h (a.) how much time is spent on the trip and (b.) how far does the person travel?
Need help finding the starting point to this equation

Respuesta :

coolstick
To start off, we have to find the difference between 89.5 and 77.8, which is 11.7. 11.7/89.5 is the fraction of the total time spent on the trip, so 22*89.5/11.7 is the total time spent which is about 168.29 minutes. to find how long the person travels for, we first have to find the average speed per minute, which is 77.8/60. After that, we multiply that by the answer we got for the time which in total approximately equals 218.22 miles

Answer:

Part a)

[tex]t = 147.8 min[/tex]

Part b)

[tex]d = 220.2 km[/tex]

Explanation:

Speed of the trip of the person is given as

[tex]v = 89.5 km/h[/tex]

here let say the time taken by the person for the trip is "t" min

so the total distance moved by the person in above time is given as

[tex]d = (89.5)\times \frac{t}{60}[/tex]

so we will have

[tex]d = 1.49 t[/tex]

now the average speed for the whole trip is given as

[tex]v_{avg} = \frac{distance}{time}[/tex]

[tex]time = t + 22 min[/tex]

now we have

[tex]v_{avg} = \frac{1.49 t}{\frac{(t + 22)}{60}}[/tex]

now we have

[tex]77.8 = \frac{1.49 t}{\frac{(t + 22)}{60}}[/tex]

[tex]1.2967(t + 22) = 1.49 t[/tex]

[tex]0.193 t = 28.53[/tex]

[tex]t = 147.8 min[/tex]

Part b)

Total distance moved by the person is given as

[tex]d = 1.49 t[/tex]

[tex]d = 1.49(147.8)[/tex]

[tex]d = 220.2 km[/tex]

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