a car is 500 miles away from its destination after 2 hours and 410 miles from its destination after 3.5 hours. What is the rate of change
a. 1.5 mph
b. 60 mph
c. 90 mph
d. 135 mph

Question

a car is 500 miles away from its destination after 2 hours and 410 miles from its destination after 3.5 hours.  What is the rate of change
a. 1.5 mph
b. 60 mph
c. 90 mph
d. 135 mph

mathstudent55 · Answer

In this problem, the rate of change is speed.
Notice all options are in mph, miles per hour.
That means you need to divide a distance (in miles) by a time (in hours).

Find the distance the car traveled between the two given points.
Find the time it took to travel that distance.
Then divide the distance by the time.

tanabugg · Answer

Wait when I divide 410 by 3.5 it gives me 117 and 410 by 2 it gives me 205

tanabugg · Answer

500-410 = 90.

mathstudent55 · Answer

Forget your first answer.

Your second answer is the correct way to start.
You subtract the distances.
The car was 500 miles away at the first point. 
Then at the second point the car was 410 miles away. 
That means it traveled 500 - 410 = 90 miles.

Now we know the distance we will use to divide it 90 miles.

mathstudent55 · Answer

Now you need to find the time it took to travel the 90 miles.

mathstudent55 · Answer

The first point is after traveling 2 hours.
The second point is after traveling 3.5 hours.
How much time is there between 2 hours and 3.5 hours of travel?

tanabugg · Answer

1.5 hrs

tanabugg · Answer

90/ 1.5 = 60

tanabugg · Answer

So it'd be b?

mathstudent55 · Answer

|dw:1478265470530:dw|

tanabugg · Answer

Was I right?

mathstudent55 · Answer

500 mi - 410 mi = 90 mi
3.5 h - 2 h = 1.5 h

$speed = rate~of~change = \dfrac{90~mi}{1.5~h} = 60 ~\dfrac{mi}{h} = 60~mph$

mathstudent55 · Answer

You are correct.

tanabugg · Answer

Yay!  Thank you so much!  I understand it now!!

mathstudent55 · Answer

Let me just add a quick note here.

mathstudent55 · Answer

Notice that the time if travel is from the start. The car is first 2 hours from the start and then 3.5 hours from the start.
The distance is from the end. The car is first 500 miles from the end and then 410 miles from the end.

In this case the fact that the time and the distance are measured from two different points of the travel, the start and the end, it really does not matter because all you need is the distance the car traveled and the time it took.

mathstudent55 · Answer

You're welcome.