Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Rational Expressions And Equations
Introduction: Real-World Applications
Rational equations frequently model real-world situations involving rates, work, and time. When two people work together, their combined rate is the sum of their individual rates. This relationship forms a rational equation.
Work Rate Formula
If one person completes a job in ahours, their work rate is 1ajobs per hour. If another person completes the same job in bhours, their rate is 1b. Working together, their combined rate is:
1a+1b=1t
where tis the time it takes them working together.
Example 1: Two Workers Together
Mario can clean a car in 6 hours. Bill can clean a car in 5 hours. How long will it take them working together?
Step 1: Set up the equation
16+15=1t
Step 2: Multiply by LCD 30t
5t+6t=30 11t=30
t=3011≈2.727hours
Step 3: Convert to hours and minutes