Rate and Ratio Word Problems Study Guide

Worksheet: Rate & Ratio Word Problems

Problem 1: Boy and Pie Consumption

  • Scenario: A boy and a half eats a pie and a half in a day and a half.
  • Question: At this rate, how many days does it take one boy to eat one pie?
  • Solution Approach:
    • Step 1: Define the consumption rate of one boy.
    • Calculation: If 1.5 boys eat 1.5 pies in 1.5 days, then each boy eats 1 pie (because 1.5 pies / 1.5 boys = 1 pie per boy) in 1.5 days.
    • Step 2: To find how many days it takes one boy to eat one pie, set the ratio such that 1 boy eats 1 pie in 1.5 days.
    • Conclusion: One boy takes 1.5 days to eat one pie.

Problem 2: Painters and Room Painting

  • Scenario: Three painters can paint three rooms in three hours.
  • Question: At this rate, how long would it take one painter to paint one room?
  • Solution Approach:
    • Step 1: Define the painting rate of one painter.
    • Calculation: Each painter paints 1 room in 3 hours (because 3 rooms / 3 painters = 1 room per painter), thus, three painters take 3 hours to complete.
    • Conclusion: Therefore, one painter takes 9 hours to paint one room (3 hours for 1 room multiplied by 3).

Problem 3: Machines and Widget Production

  • Scenario: Two and a half machines produce five widgets in two hours.
  • Question: At this rate, how many hours would it take one machine to produce one widget?
  • Solution Approach:
    • Step 1: Identify the production rate of one machine.
    • Calculation: If 2.5 machines produce 5 widgets in 2 hours, then 1 machine produces 2 widgets in 2 hours (5 widgets / 2.5 machines). Thus, it takes 1 hour to produce 1 widget.
    • Step 2: Therefore, 1 machine will take 1 hour to produce 1 widget.

Problem 4: Bakers and Cake Baking

  • Scenario: Four bakers bake eight cakes in six hours.
  • Question: At this rate, how many hours does it take one baker to bake one cake?
  • Solution Approach:
    • Step 1: Determine the rate of one baker.
    • Calculation: If 4 bakers bake 8 cakes in 6 hours, then 1 baker bakes 2 cakes in 6 hours (8 cakes / 4 bakers). Thus, to bake 1 cake takes 3 hours (6 hours for 2 cakes).
    • Conclusion: Hence, it takes 3 hours for one baker to bake one cake.

Problem 5: Gardeners and Lawn Mowing

  • Scenario: Five gardeners can mow five lawns in ten hours.
  • Question: How many hours would it take one gardener to mow one lawn?
  • Solution Approach:
    • Step 1: Establish the mowing rate of one gardener.
    • Calculation: If 5 gardeners mow 5 lawns in 10 hours, then each gardener mows 1 lawn in 10 hours (5 lawns / 5 gardeners exists the ratio).
    • Conclusion: Therefore, it takes 10 hours for one gardener to mow one lawn.

Problem 6: Typists and Page Typing

  • Scenario: One and a half typists can type nine pages in three hours.
  • Question: How long would it take one typist to type one page?
  • Solution Approach:
    • Step 1: Define the typing rate of one typist.
    • Calculation: If 1.5 typists can type 9 pages in 3 hours, then 1 typist can type 6 pages in 3 hours (9 pages / 1.5 typists). Therefore, to type 1 page takes 0.5 hours (3 hours for 6 pages).
    • Conclusion: Hence, it takes 0.5 hours (or 30 minutes) for one typist to type one page.