Distance, Rate and Time
In this lesson we will be learning how to use one of the most basic mathematical formulas:
The Distance Formula
Distance (D) = rate (r) x time (t)
 

 The first step in a distance problem is to read the problem carefully to determine which two (2) pieces of information
have been given.
In this problem we were given the rate (r) of 45 mph, and the time (t) of 3.5 hours.
The beauty of using a formula is that it tells us exactly what to do.
D = (r)(t)

Plug in the given information:

D = (45)(3.5)
Perform the indicated operation (multiplication)

D = 157.5 miles

Joe drove his car a total of 157.5 miles!

             Again, let's first find the 2 pieces of given information:
That's right, the Distance (D) is 1920 miles, and the rate (r) is 320 mph.  The missing piece in this problem is the time (t).

Now, before we can do this problem we have to convert the Distance formula: D = (r) x (t) to a formula for
finding the time.  To do this we need to divide both sides of the formula by "t".  When we do that the "r" will be all by itself, and the formula will look like this:
D/t = r
In algebra we prefer the letter we are solving for to be on the left side of the equation, so all we have to do is flip the equation around and we get:
r = D/t
Once we've done that we simply "plug in" the given information, and perform the indicated operation, which in this
formula is division.

r = 1920/320
1920/320 = 6
r = 6

So, it took the plane 6 hours to travel that distance!

Are you getting the idea?  That's right!  Find the
given information!
190 represents the Distance (D), and 5 represents
the time (t).
That means that the missing piece in this problem
is the rate (r)

Do you remember what to do from the last problem?
You got it!  We need to convert the Distance formula to a formula which allows us to solve for "r".

D = (r) x (t)
If we divide both sides by "t" it will give us "r" all by itself, and that's exactly what we need!

D/t = r
Now flip the equation around...
r = D/t
"Plug in" the given information:

r = 190/5
190/5 = 38
r = 38

The average rate the man drove on his trip was 38 mph!