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.
- 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.
- 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