AlgebraStructure & Method · Book 1All Chapters

Mixture and Work Problems

7-8Work Problems

Overview

If a job takes a hours alone, the rate is 1/a per hour. Combined rates add.

Key ideas

  • Rate · time = work done.
  • Together: 1/a + 1/b = 1/t.
  • Solve fractional equation for t.

Worked examples

Example 1

Problem. Pipe A fills a tank in 6 h; pipe B in 4 h. How long together?

Solution. 1/6 + 1/4 = 1/t → 5/12 = 1/t → t = 12/5 = 2.4 h.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    A alone: 3 h, B alone: 6 h. Together?

  2. 2.

    Together they take 2 h; A alone takes 5 h. Find B alone.

  3. 3.

    Two painters: 4 h and 6 h. Together?

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Pipe A fills a tank in 6 hours; Pipe B empties it in 8 hours. How long to fill the tank with both open?

  2. 2.

    Mary can paint a room in 4 hours; John in 6 hours. How long together?