282 algebra De mystif ieD
PRACTICE- Neil can paint a wall in 45 minutes; Scott, in 30 minutes. If Neil begins
painting the wall and Scott joins in after 15 minutes, how long will it
take both to finish the job? - Two hoses are used to fill a water trough. Hose 1 can fill it in 20 minutes
while Hose 2 needs only 16 minutes. If the Hose 2 is used for the first
4 minutes and then Hose 1 is also used, how long will Hose 1 be used? - Jeremy can mow a lawn in one hour. Sarah can mow the same lawn in
one and a half hours. If Jeremy works alone for 20 minutes then Sarah
starts to help, how long will it take for them to finish the lawn? - A mold press can produce 1200 buttons an hour. Another mold press
can produce 1500 buttons an hour. They need to produce 45,000
buttons.
(a) How long will be needed if both presses are used to run the job?
(b) If the first press runs for 3 hours then the second press joins in, how
long will it take for them to finish the run?
✔SOLUTIONS
- Neil worked alone for^1545 =^13 of the job, so^1 −=^1323 of the job remains.
Let t represent the number of minutes both will work together.
Worker Quantity Rate Time
Neil 1 1/45 45
Scott 1 1/30 30
Together 2/3^2
3
23 2
3ttt=t^The equation to solve is 451 += 301 32 t. The LCD is 90t.1
451
302
3
90 1
451
3090 2
3
90 1
45+=
+
=
t
tt
t
t
+
90 1 =
30t 60PRACTICE- Neil can paint a wall in 45 minutes; Scott, in 30 minutes. If Neil begins