The document provides examples of work, mixture, and motion problems along with explanations of the principles and formulas used to solve them. Various word problems are presented involving topics like pumps filling tanks, laborers completing jobs, mixtures of substances at different percentages, and distances traveled given rates and times. Step-by-step workings are shown for calculating answers to each problem using appropriate formulas and algebraic reasoning.

1. WORK
PROBLEM
S

2. 1
RATE
time to finish the work
If a man could finish a job in x
days, then in one day he could
1 finish only
x (rate)of the job.

3.  WORK DONE = RATE X TIME
 If both x and y are the number of days each
man work alone, then if they work together
they could finish it in “t” days.
1 1
t 1
x y

4. Answer: 7.095 hours
A pump can pump a tank in 11 hours.
Another pump can pump out the
same tank in 20 hours. How long will
it take both pumps together to pump
out the tank?

5. Answer: 12 days
 A laborer can finish a job in 4 days.
Another laborer can finish the same
job in 6 days. If both laborers plus a
third laborer can finish the job in 2
days, how long will it take for the third
laborer to finish the job alone?

6. Answer: 6 hours
 A tank is filled with an intake pipe that
will fill it in 4 hours and an outlet pipe
that will empty it in 12 hours. If both
pipes are left open, how long will it
take to fill the empty tank?

7. AB
Answer:
A B
 If A can do the work in “x” days
and B in “y” days, how long
will they finish the job?

8. Answer: 10 min.
 Mr. Brown can wash his car in 15
minutes, while his son John takes
twice as long to do the same job. If
they work together, how many
minutes can they do the washing?

9. Answer: 9 days
 It takes Butch twice as long as it
takes Dan to do a certain piece of
work. Working together they can do
the work in 6 days. How long would it
take Dan to do it alone?

10. MIXTURE
PROBLEM
S

11. PRINCIPLE:
 Sum of the values of the component parts of a
mixture is equal to the total value of the
mixture.
Example: mixture of nuts
(cost/kg)( # of kg of peanut)+ (cost/kg)(# of kg of cashew
nuts) =
(cost of the mixture/kg)(# of kg of peanut +# of kg of cashew
nuts)

12. Answer: 200 lbs.
 How many pounds of cream
containing 12% butterfat must be
added to 1800 lbs. of milk
containing 2% butterfat to obtain
a milk having 3% butterfat?

13. Answer: 20 gallons
 Two alcohol solutions consists of a 40 gallons
of 35% alcohol and other solution containing
50% alcohol. If the two solutions are combined
together , they will have a mixture of 40%
alcohol. How many gallons of the solutions
containing 50% alcohol?

14. Answer: 11 pcs of 20 peso-bill and
10 pcs of 1 peso coins
 Leslie’s coin purse contains 20
peso-bills and 1 peso coins
totaling to 230 pesos. How many
of each denomination are in her
coin purse if she has 21 pieces in
all?

15. Answers: peanuts=20 and
corn=100
 Peanuts are sold for 80 pesos per kilogram
and corn for 32 pesos per kilogram. How many
kilograms of each should be mixed to form 120
kg of a mixture than can be sold for 40 pesos
per kilogram?

16. MOTION
PROBLEM
S
D=RxT