Question

A Honda takes ten minutes to go from milepost 71 to milepost 81. A Toyota takes fifteen minutes to go from milepost 65 to milepost 80. Which car has the greater average speed?
A) The Honda
B) The Toyota
C) The average speeds are the same
D) We need to know the acceleration to answer the question.

Answer 1

The average speed of either car will be the ratio of the total distance covered by the car to the total time taken. The average speed is a scalar quantity and so will always remain positive and it does not specify the direction in which the car moves. The average speed will be greater for that car which covers more distance in a lesser amount of time.

Formula used:
-The average speed of a body is given by, ${v_{avg}} = \dfrac{d}{t}$ where $d$ is the total distance covered and $t$ is the time taken to cover the distance.

Complete step by step answer.
Step 1: List the parameters obtained from the question.
As it is mentioned, the Honda travels from milepost 71 to 81 and so the distance covered by the Honda will be ${d_H} = 81 - 71 = 10{\text{miles}}$ .
Similarly, the Toyota is mentioned to travel from milepost 65 to 80 and hence the distance covered by the Toyota will be ${d_T} = 80 - 65 = 15{\text{miles}}$ .
The time taken by each car to cover these distances are given to be ${t_H} = 10{\text{min}}$ and ${t_T} = 15{\text{min}}$ .
Step 2: Express the average speed of each car.
The average speed of the Honda can be expressed as ${v_{H.avg}} = \dfrac{{{d_H}}}{{{t_H}}}$ -------- (1)
Substituting for ${d_H} = 10{\text{miles}}$ and ${t_H} = 10{\text{min}}$ in equation (1) we get, ${v_{H.avg}} = \dfrac{{10}}{{10}} = 1{\text{miles/min}}$ .
Thus the average speed of the Honda is ${v_{H.avg}} = 1{\text{miles/min}}$.
The average speed of the Toyota can be expressed as ${v_{T.avg}} = \dfrac{{{d_T}}}{{{t_T}}}$ -------- (2)
Substituting for ${d_T} = 15{\text{miles}}$ and ${t_T} = 15{\text{min}}$ in equation (2) we get, ${v_{T.avg}} = \dfrac{{15}}{{15}} = 1{\text{miles/min}}$ .
Thus the average speed of the Toyota is ${v_{T.avg}} = 1{\text{miles/min}}$.
So both cars have the same average speed.

Thus the correct option is C.

Note: Here the Toyota covers more distance than the Honda but takes more time in doing so. The total distance covered by each car will be the difference in their final position and initial position. The direction in which each car moves is provided by the average velocity. Here the acceleration of the car is not necessary to determine its average speed.