404 algebra De mystif ieD
- Let t represent the number of hours Printing Press II needs to print the
run by itself. Because Printing Press I needs 5 fewer hours than Printing
Press II, t − 5 represents the number of hours Printing Press I needs to
complete the run by itself.
Worker Quantity Rate Time
Press I 1 1
t− 5
t − 5
Press II 1 1
t
t
Together 1 1
6
6
The equation to solve is^1
5
11
tt 6
.
–
+ = The LCD is 6t(t − 5).
1
5
11
6
651
5
651 651
6
6
tt
tt
t
tt
t
tt
t
−
+=
−⋅
−
+−⋅= −⋅
+
() () ()
665 5
66305
12 30 5
017
2
2
2
()()ttt
tt tt
ttt
t
−=−
+−=−
−=−
=−tt
tt
+
=− −
30
01 () 52 ()
t − 15 = 0 t − 2 = 0 (This cannot be a solution because
t = 15 t = 2 2 − 5 is negative.)
Printing Press II can print the run alone in 15 hours and Printing Press I
needs 15 − 5 = 10 hours.
- Let t represent the number of hours Pipe II needs to fill the reser-
voir alone. Pipe I needs 1 hour 40 minutes less to do the job, so
tt – 114060 = – 32 = t – 35 represents the time Pipe I needs to fill the reservoir
by itself.