Answer:
A) The average speed for the trip is [tex]v_{average} =53,53\frac{km}{h}[/tex].
B) The total distance traveled is [tex]d_{total}=91\ km[/tex].
Explanation:
Knowing that 1 hour has 60 minutes, we have that for each part of the trip:
[tex]v_{1}=80\frac{km}{h}\ t_{1}=0,5\ h[/tex]
[tex]v_{2}=105\frac{km}{h}\ t_{2}=0,2\ h[/tex]
[tex]v_{3}=40\frac{km}{h}\ t_{3}=0,75\ h[/tex]
[tex]v_{4}=0\frac{km}{h}\ t_{4}=0,25\ h[/tex]
Total distance traveled
The distance traveled is the speed multiplied by a period of time. The total distance traveled is calculated adding up the speeds multiplied by the given periods of time.
[tex]d_{total}=d_{1}+d_{2}+d_{3}[/tex]
[tex]d_{total}=v_{1}.t_{1}+v_{2}.t_{2}+v_{3}.t_{3}[/tex]
[tex]d_{total}=80\frac{km}{h}.0,5\ h+105\frac{km}{h}.0,2\ h+40\frac{km}{h}.0,75\ h[/tex]
[tex]d_{total}=40\ km+21\ km+30\ km[/tex]
[tex]d_{total}=91\ km[/tex]
B) The total distance traveled is [tex]d_{total}=91\ km[/tex].
Average speed
The average speed could be calculated using the total distance traveled [tex]d_{total}[/tex] divided by the total time [tex]t_{total}[/tex]. We need to take into account the time spent eating lunch and buying gas.
[tex]v_{average}=\frac{d_{total}}{t_{total}}[/tex]
[tex]v_{average}=\frac{v_{1}.t_{1}+v_{2}.t_{2}+v_{3}.t_{3}+v_{4}.t_{4}}{t_{1}+t_{2}+t_{3}+t_{4}}[/tex] [tex]v_{average}=\frac{91\ km}{0,5\ h+0,2\ h+0,75\ h+0,25\ h}[/tex]
[tex]v_{average}=\frac{91\ km}{1,70\ h}[/tex]
[tex]v_{average}=53,53\frac{km}{h}[/tex]
A) The average speed for the trip is [tex]v_{average} =53,53\frac{km}{h}[/tex].
