Age Problems

Example: Sarah is 3 times as old as Tom. In 5 years, Sarah will be twice as old as Tom. How old are they now?

Tip: Let x = Tom's current age. Then Sarah's age = 3x. Set up equation for 5 years from now.

Distance/Rate/Time Problems

Example: A train travels 240 miles in 4 hours. What is its average speed?

Formula: Distance = Rate × Time (D = RT)

Mixture Problems

Example: How much 20% salt solution must be mixed with 60% salt solution to get 10 liters of 35% solution?

Tip: Track amount of pure substance in each mixture

Work/Rate Problems

Example: Pipe A fills a pool in 6 hours, Pipe B in 4 hours. How long to fill together?

Formula: Combined rate = Rate A + Rate B

Addition (+)

sum, total, more than, increased by, added to, combined, altogether

Subtraction (−)

difference, less than, decreased by, minus, fewer, reduced by

Multiplication (×)

product, times, of, multiplied by, twice, double, triple

Division (÷)

quotient, divided by, ratio, per, out of, split evenly

Draw Diagrams

Visual representations help clarify relationships and make problems easier to understand.

Check Units

Make sure all units are consistent (hours vs minutes, meters vs feet) before solving.

Verify Answer

Plug your answer back into the original problem to confirm it makes sense.

Practice Regularly

The more word problems you solve, the better you'll recognize patterns and strategies.