WORD PROBLEMS IN ALGEBRA
General Description: Two objects travel toward or away from each
Key to solving: Distances are added together to get total distance
The distance between towns A and N is 750 kilometers. If a passenger train
leaves town A traveling toward town B at 90 kph while at the same time a
freight train leaves town B traveling towards town A at 35 kph, how long
will it take the two trains to meet?
Two cars leave Chicago at the same time and travel in opposite directions.
If one travels at 62mph and the other at 88kph, how long will it take them to
be 450 miles apart?
General Description: Two objects leave the same place and travel in the
same direction. They leave at different times. Find when the two objects
Key to solving: For an object to catch up, the distances must be equal. Set
the distances or r•t part of the equation equal to each other and solve. Times
are different and must be expressed as t for one object and t plus or minus
the difference in travel time for the other object.
A car leaves a city traveling at 60 kph. How long will it take a second car
traveling at 80 kph to catch up to the first car if it leaves two hours later?
Students are traveling in two cars to a football game 150 miles away. The
first car leaves on time and travels at an average speed of 48 mph. The
second car starts ½ hour later and travels at an average speed of 58 mph. At
these speeds, how long will it take the second car to catch up with the first
General Description: Two liquids are mixed each composed of a set
percentage of some other liquid. When mixed, they form a new
percentage of the other liquid.
Key to solving: Add together to total amount of the other liquid in each
mixture to find the total amount of the other liquid in the final mixture.
A pharmacist needs to strengthen a 20% alcohol solution so that it contains
36% alcohol. How much pure alcohol should be added to 240 ml of the
Lynn’s Dairy mixed two grades of milk to obtain 150 gallons of a 1%
butterfat mixture(new lowfat). One milk contains 0% butterfat(nonfat) while
the other contains 4% butterfat(whole milk). How many gallons of each kind
were used in the mixture?
General Description: Two kinds of dry objects selling for different
amounts are mixed together and sold for a new amount.
Key to solving: Add together the total cost for each object to obtain the total
cost for the mixture.
A grocer mixes two kinds of nuts costing $3.88 per pound and $4.88 per
pound to make 100 pounds of a mixture costing $4.33 per pound. How
many pounds of each kind of nut were put in the mixture?
A floral shop creates a mixed arrangement of roses at a cost of $1.25 each
and carnations costing $0.75 each. An arrangement of 1 dozen flowers costs
$11.00. Determine the number of roses per dozen flowers in the
General Description: Two objects perform a job at different rates. How
long does it take them to perform the job working together?
Key to solving: The rate of each object can be found by dividing the number
of jobs by the number of hours to find how much of the job can be
completed in 1 hour (the rate). The two totals (amount•rate) are then added
together and set equal to the total number of jobs completed.
Machine A can produce 2000 pounds of paper in 4 hours. Machine B is
newer and faster and can produce 2000 pounds of paper in 2 ½ hours. How
long will It take the two machines working together to produce 2000 pounds
Suppose you can mow a lawn in 3 hours and your friend can mow it in 4
hours. How long will it take both of you to mow the lawn together?