Vogt’s “Combined Work Word
Problems”
1.) One printer can label an entire high school
class list of envelopes in 4 hours, but the new printer can do the job in 2
hours. How long will it take to do the
task if both printers are used simultaneously?
2.)
One contractor can paint the campus in 6 days, another can do it in 4 days, and
still another can do it in 8 days. How long would it take to do the job if all
three contractors were hired to work together (theoretically)?
3.)
In 12 minutes,
when setting up for a party, a worker in a diner can walk around an immensely
large circular table (used for corporate round table meetings and other large
groups wanting to share a single table allowing each person a view of everyone
else) and place a plate and a cup in each
position corresponding to a seat. A co-worker can walk around the same table
removing the plate and cup from each position corresponding to a seat and clear
the table in 20 minutes. If a miscommunication results in the two performing
their duties at the same time (the worker walks around the table placing the
settings while the co-worker walks around the table removing the settings) how
long will it take to completely set the table (and when the worker reaches the
co-worker they both stop working on the table and talk)?
Fulcrum problems
4)
A 16’ bar has a fulcrum (a 3” iron pipe) positioned 1’ from its end (right hand
side). How much pressure (weight) must be applied to the end of the left hand
side to move a boulder atop the right hand side weighing 3000 lbs (a ton and a
half)?
5)
A 16’ beam is situated on top of a fulcrum resting at its middle. If a 30 lb
child sits at the left end how far in (from the right) will a 120 lb mother
have to sit so it balances?
6)
A 18’ beam will have a 20 lb weight at its left end and a 100 lb weight at its
right end, where will the fulcrum be positioned (from the right end) to balance
the two sides?
7)
A 16’ beam will have an 30 lb weight at its left end & a 120 lb weight at
its right end, where will the fulcrum be placed (give both left & right
distances) to balance the sides?
Mark-up / Discount Problems
8)
A plumber friend tells you he will do all your bathroom work and only charge
you 35% more than the cost of the supplies (which you will pay for in the final
bill). If he charges you $324, how much did he actually make? {hint: start by finding the cost of the supplies and then
subtract that cost from the final bill}
9)
The clerk at a jewelry store informs you that the boss just reduced prices 5%
from already low prices. A ring you are interested in is priced at $1172.30 and
you are wondering if the discount was significant, how much was was it priced before the discount? So, how much was the
price lowered?
10)
Pat confides in you that all the employees at Pat’s spouse’s work had their
hours cut by 15% (“across the board”),
and though working 51 hours a week (at minimum wage) Pat doesn’t know how
they’ll make ends meet. How many hours a week was Pat’s spouse working
originally? If minimum wage is $9/hr, how much did
they lose from their weekly income?
1) 1 hr 20 min 2) ≈ 1 hr
51 min 3) ½ hour
* Vogt Educational Materials
4)
200 lb 5)
6’ 6) 3’ 7) 12.8’ and 3.2’
8) $240 9)
$1,234 10) 60; $81
