Ray's New Elementary Algebra · Art. 156 (problems 41–70) · Unit 4: Chapter IV: Simple equations
29. Word problems: travel, ages and more
Goal: Your student solves a wider range of one-unknown problems, including meeting and overtaking travelers.
You'll need
- The book, open to the page
- Pencil and plenty of paper (or a whiteboard)
- A card to cover printed answers
What's in the book
Exercises 41 to 70: travelers meeting and overtaking, number puzzles, estates and capital, pipes and workers, a steamboat, mixtures and distances. All answers are printed. A general review follows.
The lesson, step by step
Warm-up
Ask: If one man walks 20 miles a day and another 30, toward each other, how much closer do they get each day? (50 miles.)
Meeting
Work together:
41. Two men set out at the same time, one from London, the other from Edinburgh; one goes 20, the other 30 miles a day ; in how many days will they meet, the distance being 400 miles? Ans. 8 days.
Equation: 20x + 30x = 400.
Overtaking
Exercise 42: B has a 10-hour start at 3 miles an hour; A goes 5. When A catches up they have gone equal distances: 5x = 3(x + 10). So x = 15 hours.
Working backward
Your student does this one while you watch:
45. If I multiply a certain number by 7, add 3 to the product, divide this by 2, and subtract 4 from the quotient, the remainder is 15. What is the number? Ans. 5.
Independent practice
Choose ten of exercises 43 to 70. Good ones: 46, 54, 55, 59, 60, 63, 64, 66 and 67.
Review
Use the General Review on p. 113 as an oral quiz on the whole chapter so far.
Wrap-up
Ask your student which kind of problem was hardest today, and why.
Tip
Drawing a line with the two travelers marked on it makes every travel problem easier.
Answers to the book's problems
The book prints the answer after each exercise.
Worked out for this site from the scan. If a number in your copy differs, trust the book. Every answer is in the Key ↗.