Question

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

Answer 1

Explanations & Calculations

• From the details of the car's motion, you can form a relationship between the total distance and the total of its time.

$\qquad\qquad \begin{aligned} \small T_c&=\small t_1+t_2\\ &=\small \frac{h/2}{40}+\frac{h/2}{80}\\ &=\small \frac{3h}{160}\cdots\cdots\cdots(1) \end{aligned}$

• From those given for the truck you can think between the total distance and the total time.

$\qquad\qquad \begin{aligned} \small h&=\small h_1+h_2\\ &=\small 40.\frac{T_t}{2}+80.\frac{T_t}{2}\\ &=\small 60T_t\cdots\cdots\cdots(2) \end{aligned}$

• Upon replacement of the total distance, you can compare the time for each one.

$\qquad\qquad \begin{aligned} \small T_c&=\small \frac{3}{160}.60T_t\\ \small T_c&=\small \frac{9}{8}.T_t\\ \therefore\small T_c &>T_t \end{aligned}$

• The truck got there in the shortest period of time.