Solving Work Problems with Rational Equations
Learn how to solve work problems involving rational equations. Find the least common denominator, multiply by it, and solve for the variables. Practice examples like determining how long it takes workers to finish a task when working together. Also, solve distance equals rate times time problems to find speeds needed to meet at a specific time.
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10.7 Solving Rational Equations in Word Problems -Work Problems -D=RT Problems
Work Problems A is worker a B is worker b C is worker a and b working together 1 a 1 b 1 c + =
Steps to Solve 1. Find the LCD 2. Multiply every term by the LCD/1 3. Solve for the variable
Example of Work Problem Nolan can eat a bag of popcorn in 2 minutes. Madison can eat a bag of popcorn in 3 minutes. If Nolan and Madison go to the movies together and share a bag of popcorn how long will it take them to finish? Nolan (worker A) = 2 minutes Madison (worker B)= 3 minutes Together (C) = x minutes 1 2 1 3 1 x + = 6 1 2 + 6 1 3 = 6 1 x x x x + = 1 3 1 1 2 6 1 5 x 6 5 x x = 1 min and utes
D=RT Steps 1. Create a chart for d =rt 2. Solve for the variable that is the same for both parties 3. Set the equations equal to each other
Example of D=rt Kylie and Peyton are going to do a flash mob. Kylie lives 1 mile away and Ella lives 5 miles away. What speed do they need to travel if they leave at the same time given that Kylie walks and Ella runs 10 mph faster then Kylie? (They want to meet at the flash mob at the same time) 1 r 5 + = ( + 5 2 10) = 1 2 r D r t D r = t 10 5 r r r t t 1 r 5 10) + 1 5 Kylie = t = 2 r or mph r+ 10 Peyton = t 5 2 25 2 1 2 + = + = 10 10 12 r or mph ( r
Homework Page 458 (2-16 even, 21-24) all
