Answer:
Average speed: 86 km/h
Explanation:
Driving from San Antonio to Houston:
1st. half time: 54km/h
2nd. half time: 118 km/h
Average speed = [tex] \frac{54 \frac{km}{h}+ 118 \frac{km}{h} }{2}=86 \frac{km}{h} [\tex]
Driving way back:
1st. half time: 54km/h
2nd. half time: 118 km/h
Average speed = [tex] \frac{54 \frac{km}{h}+ 118 \frac{km}{h} }{2}=86 \frac{km}{h} [\tex]
As in both routes we have the same average speed, then the average speed for the whole trip is 86 km/h
Answer:
[tex]v_{avg} = 79.7 km/h[/tex]
Explanation:
As we move from San Antonio to Houston
let the distance is "d" from Antonio to Houston
Half the time it moves with 54 km/h and next half the time it moves 118 km/h
so we will have
[tex]54 T + 118 T = d[/tex]
[tex]T = \frac{d}{172}[/tex]
so total time is
[tex]2T = \frac{d}{86} = 0.0116 d[/tex]
now while his return journey half the distance he move with 54 km/h and next half distance with speed 118 km/h
so we have time of return journey
[tex]T' = \frac{d/2}{54} + \frac{d/2}{118}[/tex]
so now we have
[tex]T' = 0.0135 d[/tex]
now for the average speed we know that
[tex]v_{avg} = \frac{distance}{time}[/tex]
[tex]v_{avg} = \frac{d + d}{0.0116 d + 0.0135 d}[/tex]
[tex]v_{avg} = 79.7 km/h[/tex]
