Algebra Demystified 2nd Ed

278 algebra De mystif ieD

6. Worker Quantity Rate Time
   Pipe I 1 213
   1
   132

= 213

6112 = 32

Pipe II 1 313

1

133 =^313

4 13

3

(^13) =
Together 1 1/t t
The equation to solve is^2
13
+ ^3
13
= ^1
t

. The LCD is 13t.

2

13

3

13

1

13 2

13

3

13

13 1

13 2

13

+=

 +







= 











t

tt

t

t 



+ 







=

+=

=

=

13 3

13

13

2313

513

13

5

t

tt

t

t

Together the pipes can drain the reservoir in^235 hours or 2 hours

36 minutes. (^35 of hour is^35 of 60 minutes and^35 ⋅=60 36.)

Some work problems require part of the work being performed by one

worker before the other worker joins in, or both start the job and one finishes

the job. In these cases, the together quantity will not be 1. Take the time the

one worker works alone divided by the time that worker requires to do the

entire job by himself and then subtract from this 1. This number is the propor-

tion left over for both to work together. For example, if a pipe can empty a tank

in 3 hours and works alone for 1 hour, then 31 of the job is complete and^23 of

the job remains when the second begins work. The proportion of the work

remaining becomes the quantity for the “together” line.