Answer:
The average speed is 91km/hr and the total distance traveled is 91km.
Explanation:
The average speed can be defined as the quotient between the total distance traveled and the time that took.
By given, we have the speed of each interval, and their corresponding time, we just need to find the distance traveled in each interval, and sum them all
\(t=30min; v=80km/hr\)
First, we need to transform minutes to hours. We know that 1 hour equals 60 minutes.
Interval 1.
\(t=30min\frac{1hr}{60min}=\frac{1}{2}hr\)
Then, we use the definition of constant movements, assuming that's an actual constant motion
\(d=st\\d=80km/h(\frac{1}{2}hr )\\d=40km\)
Now, we do the same for the rest of the intervals
Interval 2.
\(t=12min: v=105km/hr\)
\(t=12min\frac{1hr}{60min}=\frac{1}{5} hr\)
Then,
\(d=vt\\d=105km/hr(\frac{1}{5}hr )\\d=21km\)
Interval 3.
\(t=45min;v=40km/hr\)
\(t=45min\frac{1hr}{60min}= \frac{9}{12}hr=\frac{3}{4}hr\)
\(d=vt\\d=40km/hr(\frac{3}{4} hr)\\d=30km\)
So, the total distance traveled is
\(d_{total}=40km+21km+30km= 91km\)
And the total time is
\(t_{total}=\frac{1}{2}hr+\frac{1}{5}hr+\frac{3}{4} hr= \frac{10+4+15}{20} hr=\frac{29}{20}hr = 1.45hr\)
Now, the average speed is
\(v=\frac{d_{total} }{t_{total} }=\frac{91km}{\frac{29}{20}hr }=\frac{1820km}{20hr}=91km/hr\)
Therefore, the average speed is 91km/hr and the total distance traveled is 91km.
