Work Problems

Algebra 1 · Axiom Academy

Two painters, one fence. Alone they're slow — together their rates add up. Put the combined-work formula in your hands. Alice can paint the fence alone in 6 hours ; Bob can do it alone in 4 hours . So how fast do they finish together ? Three moves with one relationship. Set Alice's solo time, hit Go, and watch the fence fill in real time — both rates piling on at once. That's 1/6 + 1/4 of the job every hour, live. Hold Alice at 6 hours and drag Bob's solo time. Add the rates, flip the sum, and read off how long the two of them take together — t = 1 ÷ (1/6 + 1/Bob) . Alice alone takes 6 hours. Bring in a helper and drag how fast they paint — watch the hours saved grow, but feel it level off: a slow helper barely changes the finish time. One relationship, three moves: feel it , solve it , weigh it . Anywhere two efforts pile onto the same job — painters on a fence , pipes filling a pool , downloads sharing a line — add the rates, flip the sum: 1/a + 1/b = 1/t , and together always beats either one alone.

This is the written version of the interactive lesson above. See the full Algebra 1 course.