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.
- 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
)