Respuesta :
Answer:
a) The person traveled 2.83 hours.
b) The person travels 220.17 kilometers.
Step-by-step explanation:
We have that the speed is the distance divided by the time. Mathematically, that is
[tex]s = \frac{d}{t}[/tex]
(a) how much time is spent on the trip and
The peron's average speed is 77.8 km/h, which means that [tex]s = 77.8[/tex]
The person distance traveled is:
22 min is 22/60 = 0.37h.
So for the time t1, the person traveled at a speed of 89.5 km/h. Which has a distance of 89.5*t1.
For 0.37h, the person was at a stop, so she did not travel. This means that the total distance is
[tex]d = 89.5t1 + 0 = 89.5t1[/tex]
The total time is the time traveling t and the stoppage time 0.37. So
[tex]t = t1 + 0.37[/tex]
We want to find t1, which is the time that the person was driving.
So
[tex]s = \frac{d}{t}[/tex]
[tex]77.8 = \frac{89.5t1}{t1 + 0.37}[/tex]
[tex]77.8t1 + 77.8*0.37 = 89.5t1[/tex]
[tex]11.7t1 = 28.786[/tex]
[tex]t1 = \frac{28.786}{11.7}[/tex]
[tex]t1 = 2.46[/tex]
The total time is
[tex]t = t1 + 0.37 = 2.46 + 0.37 = 2.83[/tex]
The person traveled for 2.83 hours.
(b) how far does the person travel?
The person traveled 2.46 hours at an average speed of 77.8 km/h. So
[tex]s = \frac{d}{t}[/tex]
[tex]77.8 = \frac{d}{2.83}[/tex]
[tex]d = 77.8*2.83 = 220.17[/tex]
The person travels 220.17 kilometers.
