The average velocity is calculated by dividing the total distance traveled by the total time. The average velocity of the total trip is 76.6km/h
Let
[tex]d \to distance[/tex]
[tex]t \to time[/tex]
[tex]v \to velocity[/tex]
When the bus travels 280km with average velocity of 88km/h, the time spent is calculated as follows:
[tex]v = \frac dt[/tex]
[tex]88 = \frac{280}t[/tex]
Make t the subject
[tex]t = \frac{280}{88}[/tex]
[tex]t = 3.2h[/tex]
When the bus travels 210km with average velocity of 75km/h, the time spent is calculated as follows:
[tex]v = \frac dt[/tex]
[tex]75 = \frac{210}t[/tex]
Make t the subject
[tex]t = \frac{210}{75}[/tex]
[tex]t = 2.8h[/tex]
The total distance of the trip is:
[tex]d = 280km + 210km[/tex]
[tex]d = 490km[/tex]
The total time spent is:
[tex]t = 3.2h + 24min + 2.8h[/tex]
Convert to hours
[tex]t = 3.2h + 24/60h + 2.8h[/tex]
[tex]t = 3.2h + 0.4h + 2.8h[/tex]
[tex]t = 6.4h[/tex]
So, the average velocity (v) is:
[tex]v = d \div t[/tex]
[tex]v = 490km \div 6.4h[/tex]
[tex]v = 76.6km/h[/tex]
Hence, the average velocity of the total trip is 76.6km/h
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