Algebra Demystified 2nd Ed

404 algebra De mystif ieD

3. 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.

4. 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.