8-6 Solving Rational Functions Today’s Objective: I can solve a rational equation.

You normally walk the sidewalk from home to school in 25 minutes. If you walk the shortcut at your normal rate, how much time would you save? 𝑊𝑎𝑙𝑘𝑖𝑛𝑔 𝑅𝑎𝑡𝑒= 0.5+1.2 25 =0.068 𝑚𝑖/𝑚𝑖𝑛 𝑆ℎ𝑜𝑟𝑡𝑐𝑢𝑡 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒=1.3 𝑚𝑖𝑙𝑒𝑠 𝑇𝑖𝑚𝑒= 1.3 𝑚𝑖𝑙𝑒𝑠 0.068 𝑚𝑖/𝑚𝑖𝑛 ≈19 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 𝑇𝑖𝑚𝑒 𝑠𝑎𝑣𝑒𝑑=25−19=6 𝑚𝑖𝑛𝑢𝑡𝑒𝑠

Solving Rational Equations Multiply to eliminate the fractions. 6 𝑥 + 𝑥 2 =4 (2𝑥) 2 𝑥+2 + 𝑥 𝑥−2 =1 (𝑥+2)(𝑥−2) 2𝑥 6 𝑥 +2𝑥 𝑥 2 =2𝑥(4) 2(𝑥−2) +𝑥(𝑥+2) =(𝑥+2)(𝑥−2) 12 + 𝑥 2 =8𝑥 2𝑥−4 + 𝑥 2 +2𝑥= 𝑥 2 −4 𝑥 2 −8𝑥+12=0 4𝑥=0 (𝑥−2)(𝑥−6)=0 𝑥=0 𝑥=2 or 𝑥=6

I can clean my garage in 4 hours. My son, Ethan, can clean it in 9 hours. How long will it take if they work together? What fraction of the garage will be cleaned by me in 1 hour? What fraction of the garage will be cleaned by me in x hour? What fraction of the garage will be cleaned by Ethan in x hour? What expression can we write if they work together? 2 hours 45 minutes

A flight across the U.S. takes longer going west than it does going east. The time for a round trip Chicago to San Francisco (1850 miles one way) is 7.75 hours. If the airplane cruises at 480 miles per hour, what is the speed of the wind? x = the speed of the wind Distance = Rate × time 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑅𝑎𝑡𝑒 Time = 1850 480+𝑥 1850 480−𝑥 + = 7.75 Distance Rate Time Eastbound Westbound 1850 480+𝑥 𝑥=35 𝑚𝑝ℎ 1850 480 + x p.546 :14-20, 36-38, 43-45 p.526 :21-22 1850 480−𝑥 1850 480 – x

Grades You earned an 82% on your first test. How many consecutive 100% test scores do you need to bring your average up to 97%. So you don’t have to take the final. Assume that each test has equal impact on the average grade. 82 + 100𝑥 =0.97 100+100𝑥 𝑥=5

Cost over Time Problems A new High Definition TV costs $1600 and uses $15 of electricity a year. How long do I have to own the TV to have an average annual cost of $100 or less? What would be the average annual cost of owning the TV for 5 years? What would be the average annual cost of owning the TV for x years?

If Elaine is working alone, she can complete a job in 10 minutes. If she works with Jose, they can complete the job in 6 minutes. How long will it Jose to complete the job alone? Fraction of the job for Elaine in 6 minutes? Fraction of the job for Jose in 6 minutes? 15 minutes

Pg. 538 problem 5 Gas mileage