Algebra2D

Word Problems - Theory & Concepts - Work Problems

Techniques and strategies for solving common algebraic word problems including age, mixture, work, motion, and clock problems.

\frac{1}{t_A} + \frac{1}{t_B} = \frac{1}{t_{\text{together}}}

Person A Alone Time ($t_A$)4 hours

Person B Alone Time ($t_B$)6 hours

Current Time Explorer0.00 hrs

Adding the rates:

\text{Rate}_A = \frac{1}{4}, \quad \text{Rate}_B = \frac{1}{6}

\text{Combined Rate} = \frac{1}{4} + \frac{1}{6} = \frac{10}{24}

Time working together:

t_{\text{together}} = \frac{4 \times 6}{4 + 6} = 2.40 \text{ hours}

Person A (Alone - takes 4 hrs)0% Complete

Rate: 0.250 job per hour

Person B (Alone - takes 6 hrs)0% Complete

Rate: 0.167 job per hour

A & B Working Together (takes 2.40 hrs)0% Complete

Combined Rate: 0.417 job per hour

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