Algebra Demystified 2nd Ed

446 algebra De mystif ieD

spent driving from Buffalo to Detroit is^215

r +  10

. The equation to solve is
215 215
10

7

rr

+ 

+ 

= . The LCD is r(r + 10).

rr

r

rr

r

rr

r

() () ()

()

+++

+

=+

++

10215 10 215

10

107

215 10 21557 10

215 2150 215 770

430 2150 7

2

2

rrr

rrrr

rr

=+

++=+

+=

()

++

=− −

=−− ±− −−

70

07 360 2150

360 360 47 215

2

2

r

rr

r ()()()(^00

27

360 129 600 60 200

14

360 189 800

14

360

)

()

= ±+,,= ± ,

≈ ±^4 435 66

14

568 360 435 66

14

. ≈. mphi −. snotasolutionn.






The family averaged 56.8 mph from Detroit to Buffalo.

5. Let r represent the average speed on his trip from Boston to New York.
   Because his average speed was 17 mph slower on his return trip,
   r − 17 represents his average speed on his trip from New York to
   Boston. The distance between Boston and New York is 190 miles. The
   time on the road from Boston to New York is^190
   r

and the time on the

road from New York to Boston is^190

r –  17

. The time on the road from
Boston to New York plus the time on the road from New York to Boston is
8 hours 5 minutes =  605   =  121 = 88^9712 hours. The equation to solve is
190 190
17

97

rr 12

+ 

– 

= . The LCD is 12r(r − 17).

12 17190 12 17 190

17

12 1797

12

12

rr

r

rr

r

() () rr()

(

−+−

−

=−

1190 17 12 190 97 17

2280 17 2280

)( )()()

()

rrrr

rr

−+ =−

−+ = 997 1649

2280 38 760 2280 97 1649

4560 3

2

2

rr

rrrr

r

−

−+=−

−

,

88760 97 1649

097 6209 38 760

2

2

,

,

=−

=− +

rr

rr