Rate of Speed / Travel
Suzie and Brad are meeting in Orlando for the weekend. Suzie travels 320 miles in the
same time that Brad travels 270 miles. If Suzie’s rate of travel is 10 mph more than
Brad’s, and they travel the same length of time, at what speed is Suzie traveling?
Step1: Set it up
It’s a distance/rate/time problem.
Enter both Suzie and Brad’s
information into the distance
formula
(Distance = Rate X Time)
d = rt
Determine what
type of problem it is
and what formula
applies.
Suzie’s Information
Brad’s Information
Distance = rate x time
(320) = (r + 10)(t)
Ashley‘s rate of speed is
10mph more than
Devon
Distance = rate x time
(270) = (r)(t)
Ashley’s and Devon’s
time are the same.
Devon’s rate of speed is
unknown. Assign “r’ as
his rate of speed.
We now have a system of two equations:
320 = (r+10)T
270 = rt
Step 2: Decide which method to use (Should you use elimination or the substitution method?)
Use the substation method in this case because the elimination method would be much more difficult.
Suzie’s time
t
t
d
r
320
r  10
The Academic Support Center at Daytona State College (Math 34 pg 1 of 2)
Brad’s time
t
t
d
r
270
r
Rate of Speed / Travel (continued)
Since Ashley and Devon’s times are the same, we will set them equal to each other, and then
solve for “r”. Suzie’s rate will be whatever “r” is, plus 10.
Step 3: Solve the problem
320
r  10

270
r
Cross multiply to get the following equation:
320r
320r
 270 (r  10)
 270r  2700
 2700
2700
r 
50
50r
 54mph
r  10  54  10  64mph
Brad’s rate = 54mph
Suzie’s rate = 64mph
The Academic Support Center at Daytona State College (Math 34 pg 2 of 2)