Answer to Question #139934 in Mechanics | Relativity for Bell

Question

A car travels 25.0 km of a 50.0 km trip at an average speed of 40.0kmh^-1. It travels the second half of its journey at an average speed of 80.0kmh^-1. A truck makes the same trip but spends half of its time at an average speed of 40.0kmh^-1 and the other half of its time at an average speed of 80.0kmh^-1. Which vehicle got there in the shortest period of time?

Answer 1

$time = \frac{distance}{speed}$

for the car,

total time taken $=\frac{25}{40}+\frac{25}{80}=\frac{15}{16} hours=0.9375hrs$

for the truck,

let the total time taken = $x$ hours

speed $\times$ time =distance

$(\frac{1}{2}x)40+(\frac{1}{2}x)80=50$

$20x+40x=50$

$60x=50$

$x=\frac{50}{60}=0.8333hrs$

the truck took the shortest time to go there.