Algebra Demystified 2nd Ed

Chapter 11 QuaDraTiC appliCaTionS 433

The plane’s average speed without the wind would have been about
320 mph.

2. 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.