Algebra Demystified 2nd Ed

444 algebra De mystif ieD

home is^6

r –  2

. The total time is 1 hour 21 minutes =  6021   =  207 = 11^2720 hours.
The equation to solve is^66
2

27

rr 20

+ 

– 

= . The LCD is 20r(r − 2).

20 26 20 2 6

2

20 227

20

120 212

rr

r

rr

r

rr

r

() () ()

()

−+ −

−

=−

−+ 00272

120 240 120 27 54

240 240 27

2

2

rrr

rrrr

rr

=−

−+=−

−=

()

−−

=−+

=−+

=

54

027 294 240

1

3

0 1

3

27 294 240

09

2

2

r

rr

rr

r

() ()

(^229880)
0109 8
−+
=− −
r
()rr()
r − 10 = 0 9 r − 8 = 0 (This does not lead to a solution.)
r = 10
The man’s average speed on his way to work was 10 mph.

2. Let r represent the saleswoman’s average speed on her return trip. Her
   average speed on the way to the customer is r + 15. The distance each
   way is 120 miles. She spent a total of 4 hours 40 minutes =  6040   = ^23 = 44^143
   hours driving. The time spent driving to the customer is^120
   r +  15
   . The time
   spent driving on the return trip is^120
   r
   . The equation to solve is
   120
   15

120 14

rr 3

+ 

+  = . The LCD is 3r(r + 15).

315 120

15

315 120 315 14

3

360

rr

r

rr

r

rr

r

()+⋅ () ()

+

++⋅=+⋅

+++=+

++=+

360 15 14 15

360 360 5400 14 210

72

2

() ()rrr

rr rr

00 5400 14 210

014 510 5400

1

2

0 1

2

14

2

2

2

rrr

rr

r

+=+

=−−

()= ( −−−

=−−

510 5400

072 255 2700

r

rr

)