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.
- 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