Mastering Work and Time Word Problems in Algebra

The Organic Chemistry Tutor

This comprehensive math tutorial guides students through solving "work and time" algebraic word problems, ranging from basic to advanced complexity. The video introduces the fundamental work-rate formula (1/T_total = 1/T_1 + 1/T_2) and demonstrates how to apply it to various scenarios, including finding the combined time for two or more workers, calculating the time for an individual worker given the total time, and solving problems involving relative speeds (e.g., "worker A is 3 times faster than worker B"). The content explores key algebraic themes such as rational equations, finding the least common multiple (LCM) to clear denominators, and setting up systems of equations. A significant portion of the video is dedicated to translating English sentences into mathematical expressions, particularly clarifying the counterintuitive relationship between speed and time—specifically, that working "faster" means dividing the time, not multiplying it. For educators, this video serves as an excellent resource for Algebra 1 and 2 curriculums. It provides a structured approach to a notoriously difficult type of word problem. The seven distinct examples build in difficulty, allowing teachers to scaffold learning. The clear, step-by-step narration makes it suitable for direct instruction, independent review, or as a reference for flipping the classroom.