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
![s = \frac{d}{t}](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7Bd%7D%7Bt%7D)
(a) how much time is spent on the trip and
The peron's average speed is 77.8 km/h, which means that ![s = 77.8](https://tex.z-dn.net/?f=s%20%3D%2077.8)
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
![d = 89.5t1 + 0 = 89.5t1](https://tex.z-dn.net/?f=d%20%3D%2089.5t1%20%2B%200%20%3D%2089.5t1)
The total time is the time traveling t and the stoppage time 0.37. So
![t = t1 + 0.37](https://tex.z-dn.net/?f=t%20%3D%20t1%20%2B%200.37)
We want to find t1, which is the time that the person was driving.
So
![s = \frac{d}{t}](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7Bd%7D%7Bt%7D)
![77.8 = \frac{89.5t1}{t1 + 0.37}](https://tex.z-dn.net/?f=77.8%20%3D%20%5Cfrac%7B89.5t1%7D%7Bt1%20%2B%200.37%7D)
![77.8t1 + 77.8*0.37 = 89.5t1](https://tex.z-dn.net/?f=77.8t1%20%2B%2077.8%2A0.37%20%3D%2089.5t1)
![11.7t1 = 28.786](https://tex.z-dn.net/?f=11.7t1%20%3D%2028.786)
![t1 = \frac{28.786}{11.7}](https://tex.z-dn.net/?f=t1%20%3D%20%5Cfrac%7B28.786%7D%7B11.7%7D)
![t1 = 2.46](https://tex.z-dn.net/?f=t1%20%3D%202.46)
The total time is
![t = t1 + 0.37 = 2.46 + 0.37 = 2.83](https://tex.z-dn.net/?f=t%20%3D%20t1%20%2B%200.37%20%3D%202.46%20%2B%200.37%20%3D%202.83)
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
![s = \frac{d}{t}](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7Bd%7D%7Bt%7D)
![77.8 = \frac{d}{2.83}](https://tex.z-dn.net/?f=77.8%20%3D%20%5Cfrac%7Bd%7D%7B2.83%7D)
![d = 77.8*2.83 = 220.17](https://tex.z-dn.net/?f=d%20%3D%2077.8%2A2.83%20%3D%20220.17)
The person travels 220.17 kilometers.