Algebra Demystified 2nd Ed

Chapter 11 QuaDraTiC appliCaTionS 445

r=−− ±− −−

= ±+

()()()()

()

,

255 255 47 2700

27

255 65 025 75

2

,, 600 ,

14

255 140 625

14

255 375

14

45 255 375

14

= ± = ±

rr== − iisnotasolution







The saleswoman averaged 45 mph on her return trip.

3. Let r represent the couple’s average rate on their way home, then r − 0.2
   represents the couple’s average speed to the public beach. The distance
   to the public beach is 4 miles. They walked for a total of 2 hours 35 min-
   utes =  6035   =  127 = 22 1231 hours. The time spent walking to the public beach
   is^4
   r .–  02
   . The time spent walking home is^4
   r
   . The equation to solve is
   4
   02

431

rr . 12

– 

+  = . The LCD is 12r(r − 0.2).

12 02 4

02

12 024 12 0231

12

48

rr

r

rr

r

rr

r

(.)

.

− (.)(.)

−

+−=−

++−=−

+−=−

−

48 02 31 02

48 48 96 31 62

96

2

(.)(.)

..

rrr

rr rr

r 996 31 62

031 102296

2

2

..

..

=−

=− +

rr

rr

(Multiplying by 10 to clear the decimals would result in fairly large num-
bers for the quadratic formula.)

r=−− ±− −

= ±

(.)( .) ()(.)

()

.,

1022 102243196

231

102210

2

4 444 84 11904

62

1022 9254 44

62

1022962

62

1

....

..

− = ±

= ± =^66

5

3

31

3

31

,   isnotasolution.







The couple walked home at the rate of^165  .=  32 mph.

4. Let r represent the average speed from Detroit to Buffalo. The average
   speed from Buffalo to Detroit is r + 10. The distance from Detroit to
   Buffalo is 215 miles and the total time the family spent driving is
   7 hours. The time spent driving from Detroit to Buffalo is^215
   r
   . The time