Question

A car traveling on a highway is 60 miles away from home after 1 hour, and is 300 miles away from home after 5 hours. What is the rate of change of the car’s distance over time?. a. 1/60 mph. b. 15/2 mph. c. 55mph. d. 60 mph

Answer 1

Answer:

d. 60 mph.

Step-by-step explanation:

Let x be the number of hours and y be the distance covered in miles.

We have been given that a car traveling on a highway is 60 miles away from home after 1 hour, and is 300 miles away from home after 5 hours.

Since distance covered by car depends on number of hours, so distance will be dependent variable, y.

Now we will use average rate of change formula to solve our given problem.

$\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}$

Substituting our given values in above formula we will get,

$\text{Average rate of change}=\frac{300-60}{5-1}$

$\text{Average rate of change}=\frac{240}{4}$

$\text{Average rate of change}=60$

Therefore, average rate of the car’s distance over time is 60 miles per hour and option 'd' is the correct choice.

Answer 2

The rate of change of car’s distance over time is equal to the velocity of the car. To find the rate of change of the given conditions, we use the formula veloctity = (Distance 2 + distance 1) / (time2 + time 1). In this case, we substitute, (60 +300)miles/ (1+5) hours equal to 60 miles per hour. Answer is D. 60 mph