Algebra Demystified 2nd Ed

Chapter 11 QuaDraTiC appliCaTionS 431

Pittsburgh to Miami is^1000
r +  50

. The time in the air from Miami to Pittsburgh

plus the time in the air from Pittsburgh to Miami is 4^12 = 4.5 hours. The equa-

tion to solve is^1000
50

1000

50

45

rr

 .

– 

+ 

+ 

= . The LCD is (r – 50)(r + 50).

()()

()() (

rr

r

rr

r

r

−+

−

+

−+

+

=−

50 50 1000

50

50 501000

50

50 ))( )( .)

()().[()(

r

rrrr

+

++ −= −

50 45

1000 50 1000 50 45 50 ++

++−=−

50

1000 50 000 1000 50 000 45 2500

200

2

)]

rr,,.(r )

00451 1 250

045 2000 11 250

2000

2

2

rr

rr

r

=−

=−−

=−− ±

.,

.,

()(()(.)( ,)

(.)

,,

−−−

= ±+

2000 4451 1 250

245

2000 4 000 000

2

2 202 500

9

2000 4 202 500

9

2000 2050

9

2000 2050

9

,,= ± ,

= ± = + ,,^20002050

9

− = 450

(–^509 is not a solution.) The plane’s average speed without the wind is
450 mph.

PRACTICE

1. A flight from Dallas to Chicago is 800 miles. A plane flew with a 40-mph
   tailwind from Dallas to Chicago. On the return trip, the plane flew
   against the same 40-mph wind. The plane was in the air a total of
   5.08 hours for the flight from Dallas to Chicago and the return flight.
   What would have been the plane’s speed without the wind?


2. A flight from Houston to New Orleans faced a 50-mph headwind, which
   became a 50-mph tailwind on the return flight. The total time in the air
   was 143 hours. The distance between Houston and New Orleans is 300
   miles. How long was the plane in flight from Houston to New Orleans?


3. A small motorboat traveled 15 miles downstream then turned around
   and traveled 15 miles back. The total trip took 2 hours. The stream’s
   speed is 4 mph. How fast would the boat have traveled in still water?

PRACTICE

1. A flight from Dallas to Chicago is 800 miles. A plane flew with a 40-mph
   tailwind from Dallas to Chicago. On the return trip, the plane flew

PRACTICE

1. A flight from Dallas to Chicago is 800 miles. A plane flew with a 40-mph