Transcript Example Cade traveled 48 miles at a certain speed. If he had gone 4 mph faster, the trip would have taken 1 hr.

Example
Cade traveled 48 miles at a certain speed. If he
had gone 4 mph faster, the trip would have taken
1 hr less. Find Cade’s average speed.
Solution
1. Introduction. As in Section 6.5, we can create a
table. Let r represent the rate, in miles per hour,
and t the time, in hours for Cade’s trip.
Distance
Speed
Time
Slower
48
r
48/r
Faster
48
r+4
48/(r +4)
2. Body
48
48
1 
.
r
r4
Solve algebraically
 48   48 
r (r  4)   1  
 r (r  4)
 r
 r 4
48(r  4)  r (r  4)  48r
48r  192  r 2  4r  48r
r 2  4r  192  0
(r  12)(r  16)  0
r  12 or r  16
Solve graphically
r  12
3. Conclusion. Cade traveled at 12 mph.
Solving Formulas
Recall that to solve a formula for a certain
letter, we use the principles for solving
equations to get that letter alone on one side.


1 2
Example Solve D  n  5n for n.
2
Solution

1 2
D  n  5n
2

2D  n2  5n
n2  5n  2D  0
a  1, b  5, c  2D
Multiplying both sides by 2
Writing standard form
5  (5) 2  4(1)(2 D) Using the quadratic
n
formula
2(1)
5  25  8D
n
2