Chapter 8 linear appliCaTionS 281

(^) Worker Quantity Rate Time
Press A 100 t 100 t
Press B 150 t 150 t
Together 150,000 150,000/t t
In this problem, the quantity produced by Press A plus the quantity
produced by Press B will equal the quantity produced together. This
gives the equation 100t + 150t = 150,000. (Another equation that
works is 100 + 150 = 150,000/t.)
100 150 150 000
250 150 000
150 000
250
600
tt
t
t
t
+=

=

,
,
,^
The presses will run for 600 minutes or 10 hours.
(b) Because Press A works alone for 24 minutes, it has run 24 × 100 =
2400 fliers. When Press B begins its run, there are 150,000 – 2400 =
147,600 fliers left to run. Let t represent the number of minutes both
presses are running. This is also how much time Press B spends on the
run. The boxes will represent work done together.
(^) Worker Quantity Rate Time
Press A 100 t 100 t
Press B 150 t 150 t
Together 147,600 147,600/t t
The equation to solve is 100t + 150t = 147,600. (Another equation that
works is 100 + 150 = 147,600/t.)
100 150 147 600
250 147 600
147 600
250
(^59025)
tt
t
t
+=

==
,
,
, == 590 .m 4 inutes
The presses will work together for 590.4 minutes or 9 hours 50 minutes
24 seconds. (This is 590 minutes and 0:4(60) = 24 seconds.)