Section 6.5 Applications of Rational Functions

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Presentation transcript:

Section 6.5 Applications of Rational Functions

I) Revisit: Speed, Time, Distance (STD) Volume of Box: Volume of a Cylinder:

Rate of Work Problems: Problems involving two or more people working together on a task: ie cutting grass, painting a house… When each person work alone, they require a certain amount of time. Asked how much time it takes if they work together. Ex: Mike can mow his lawn in 2h and his brother Tim can mow in 4h. How long will it take if they work together? % of Mike’s Work: % of Tim’s Work: It will take 4/3 of an hour if they work together

Together, Larry and Stew can do a job in 72minutes Together, Larry and Stew can do a job in 72minutes. Individually, Larry takes an hour longer than Stew. How long does it take Larry to do the job by himself?

II) Applications of Rational Expressions Flight Scheduling Time it takes a plane to travel a certain distance Turbulence Wind speed Flight schedules can be significantly affected in airports when plane speeds are changing Hartsfield-Jackson Atlanta International Airport Over 930,000 flights a year!!

EX: The distance from Vancouver to Toronto to is 3400KM EX: The distance from Vancouver to Toronto to is 3400KM. A plane travels to Toronto with a tail wind and on the way back with a constant head wind with the same wind speed. a) Find an equation for the total time of a round trip. B) If the wind speed was 50km/h how fast must the plane fly to complete a round trip in 9hours? Gather Information Equation:

b) How fast must we fly to arrive within 9 hours?

Ex: The flight distance from Vancouver to HK is 10300km Ex: The flight distance from Vancouver to HK is 10300km. If the wind speed is 60km/r, how fast must a plane fly if a round trip will take 25hours?

Time Speed

Practice: Jack and Steven are both leaving Portland for Bellingham (300km). Jack is taking the plane and Steven is driving. If Jack travels 10 times faster and requires 4.5 hours less, how fast is each person travelling? Equation: Gather Information Difference in time is 4.5h Solve for “x”

Homework: assignment 6.5