Work Rate Problems

Algebra 2 · Axiom Academy

One hose alone takes 6 hours, the other 4 — turn on both, and the combined-rate math takes over. Hose A fills the pool alone in 6 hours ; Hose B fills it alone in 4 hours — three ways to see what happens when they run together. A rate is 1 ÷ time, and rates add — they don't average (6 and 4 isn't 5). Set how long each hose takes alone, hit Go, and watch their combined rate fill the pool. The canonical case: 1/6 + 1/4 = 5/12 pool/hour, so together they finish in 12/5 = 2.4 hours. Now flip the question — pick a target finish time, and see what Hose B alone would need to be. Hose A alone takes 6 hours. Slide Hose B's own time and watch how many hours — and what percent — turning it on actually saves. Two workers, one job: rates add , times don't — 1/a + 1/b = 1/t . The same combined-rate logic runs pipes filling a tank, printers splitting a run, or crews framing a house together.

This is the written version of the interactive lesson above. See the full Algebra 2 course.