Chapter 11 QuaDraTiC appliCaTionS 435
1000 20 000 1000 20 000 55 400
2000 55
rrr^2
rr
−++=−
=
,,.( )
.^22
2
2
2200
055 2000 2200
2000 2000 4
−
=−−
=−− ±− −
.
()()(
rr
r^5552200
255
2000 4 000 000 48 400
11
2000
.)()
(.)
,, ,
−
= ±+
= ±± ≈ ± ≈
−
4 048 400
11
2000 2012 063617
11
365
2000 2012
,,. ,
. 0063617
11
isnegative
The plane would have averaged about 365 mph without the wind.
- Let r represent the plane’s average speed without the wind. The plane’s
average speed from Minneapolis to Atlanta (against the headwind) is
r − 30. The plane’s average speed from Atlanta to Minneapolis (with the
tailwind) is r + 30. The total time in the air is 512 hours and the distance
between Atlanta to Minneapolis is 900 miles. The time in the air from
Minneapolis to Atlanta is^900
r – 30
hours, and the time in the air from
Atlanta to Minneapolis is^900
r + 30
hours. The time in the air from Minne-
apolis to Atlanta plus the time in the air from Minneapolis to Atlanta is
5512 .= 5 hours. The equation to solve is^900
30
900
30
55
rr
.
–
+
+
= . The LCD is
(r − 30)(r + 30).
()rr() ()() ()(
r
rr
r
−+ r
−
+− +
+
30 30 900 =−
30
30 30 900
30
30 rr
rrrr
+
++ −= −+
30 55
900 30 900 30 55 30 30
)( .)
()().[()()]]
,,.( )
.
900 27 000 900 27 000 55 900
1800 55
rrr^2
rr
++−=−
=^22
2
2
4950
055 1800 4950
1800 1800 4
−
=−−
=−− ±− −
.
()()(
rr
r^5554950
255
1800 3 240 000 108 900
11
180
.)()
(.)
,, ,
−
= ±+=^003 348 900
11
1800 1830
11
330 1800 1830
11
±
= ± = −
,,
isnnegative
The plane’s average speed without the wind was 330 mph.