These case studies demonstrate how to apply algebraic principles to solve classic word problems methodically.

Example 1: Translating Age Relationships (Basic)

Problem: A father is three times as old as his son. In 1212 years, he will be twice as old as his son. What are their present ages?

Step-by-Step Solution

0 of 5 Steps Completed
1

Example 2: Combining Mixtures (Intermediate)

Problem: A chemist needs 5050 mL of a 30%30\% acid solution. She has a 20%20\% acid solution and a 45%45\% acid solution in stock. How many milliliters of each should she mix?

Step-by-Step Solution

0 of 5 Steps Completed
1

Example 3: Working Together (Intermediate)

Problem: Pump A can fill a tank in 44 hours. Pump B can fill the same tank in 66 hours. If both pumps work together, how long will it take to fill the tank?

Step-by-Step Solution

0 of 3 Steps Completed
1

Example 4: Catch-Up Motion (Advanced)

Problem: Train A leaves a station traveling at 6060 mph. Two hours later, Train B leaves the same station on a parallel track, traveling in the same direction at 9090 mph. How long will it take Train B to catch up to Train A?

Step-by-Step Solution

0 of 3 Steps Completed
1

Example 5: Clock Hand Overlap (Advanced)

Problem: At what exact time between 4:00 and 5:00 do the minute and hour hands of a clock overlap?

Step-by-Step Solution

0 of 4 Steps Completed
1

Caution

When working with clock hands, remember that "time" refers to the number of minutes past the hour. The hour hand also moves during this time, which is why the relative speed approach is required.

PreviousWord Problems - Theory & Concepts
Quiz Me
NextSystems of Equations - Theory & Concepts