Chapter 11 QuaDraTiC appliCaTionS 433
The plane’s average speed without the wind would have been about
320 mph.
- Let r represent the plane’s average speed without the wind. The average
speed from Houston to New Orleans (against the headwind) is r − 50,
and the average speed from New Orleans to Houston (with the tailwind)
is r + 50. The distance between Houston and New Orleans is 300 miles.
The time in the air from Houston to New Orleans is^300
r – 50
, and the time
in the air from New Orleans to Houston is^300
r + 50
. The time in the air
from Houston to New Orleans plus the time in the air from New Orleans
to Houston is 1 7
4
(^34) = hours. The equation to solve is^300
50
300
50
7
rr 4
–
+
+
= .
The LCD is 4(r − 50)(r + 50).
45050 300
50
()rr()
r
−+
−
- 45050 300
50
450507
4
1200 50
()() ()()
()
rr
r
rr
r
−+
=− +
++ 11200 50 75050
1200 60 000 1200 6
()[( )( )]
,
rrr
rr
−=−+
++− 00000 7 2500
2400 717500
07 2400 17
2
2
2
,( )
,
=−
=−
=− −
r
rr
rr,, 500
r=−− ±− −−
= ±
()()()(,)
()
,
2400 2400 47 17 500
27
2400 576
2
00000 490 000
14
2400 6 250 000
14
2400 2500
14
3
,,
,,
= ± = ±
= 550 2400 2500
14
−
isnegative
The average speed of the plane without the wind was 350 mph. We want
the time in the air from Houston to New Orleans:^300
50
300
r 350 50
–
=
–
=^
300
300
= 1 hour. The plane was in flight from Houston to New Orleans for
1 hour.