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Algebra: Work-Related Problems and Rates, Lecture notes of Mathematics

Examples and solutions for algebra problems related to work and rates, including digit-related problems and teamwork scenarios. Students will learn how to determine the time to finish a job, the rate of doing the job, and the amount of work done by individuals or teams with different rates.

What you will learn

  • What is the effect on the workload when the number of workers is reduced or increased?
  • What is the relationship between the rates of Albert and Bryan when they work together to finish a job?
  • How can Albert and Bryan's rates be determined from the number of days it takes each to finish a job?

Typology: Lecture notes

2021/2022

Uploaded on 11/26/2022

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CE 111-
BASIC CE MATH
Lesson 9
Algebra
Work-Related Problems
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CE 111-

BASIC CE MATH

Lesson 9 Algebra Work-Related Problems

LECTURE

OBJECTIVES

The primary objective of this lecture is to learn about verbal problems in algebra.

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ALGEBRA

For example: Albert can finish a job in A days Bryan can finish the same job in B days Carlo can undo the job in C days

ALGEBRA

1/A = rate of Albert 1/B = rate of Bryan -1/C = rate of Carlo

Albert and Bryan work together until the job is done:

Albert is doing the job while Carlo is undoing it until the job is done:

−^

= 1

ALGEBRA

If a job can be done by 10 workers in 5 hours, the workload is 10(5) = 50 man-hours.

If 4 workers is doing the job for 6 hours, the work done is 4(6) = 24 man-hours.

A remaining of 50 - 24 = 26 man-hours of work still needs to be done.

ALGEBRA

Example: Eleven men could finish the job in 15 days. Five men started the job, and four men were added at the beginning of the sixth day. How many days will it take them to finish the job?

Solution:

ANSWERS:

ANSWER KEYS

ANSWERS:

ANSWER KEYS