Fraction and Rational Equations Rational
Rational Equations
Rational equations can be used to get a general idea about the rate at which a job can be completed. This can be really useful for business owners and other areas of daily life.
Here is an example:
Scenario: Sue can paint the garage in 4 hours and Joe has carpal tunnel so he is slower and can paint the same garage in 6 hours. How long (number of hours) will it take Sue and Joe to paint the garage if they work together?
Solution: Sue can paint of the garage in 1 hour. Joe can paint of the garage in one hour. We don’t know how long it will take them working together, so we let x = the number of hours it takes them to paint the kitchen working together. Below is a table that relates the data from our problem. We are using the concept that (rate)(time) = fraction of the task done.
Now we can write an equation to represent: Fraction of work done by Sue in x hours + Fraction of work done by Joe in x hours = 1 job completed For your initial response:
Complete both parts.
a) Solve the rational equation in the example above. Make sure you label your answer properly and show your work.
b) Create a scenario similar to the example above and include the equation you would use to answer the question in your scenario. Ask your classmates to solve the equation. Make sure to check back at the end of the week to verify the answer to your equation!.
A. x/4 + x/6 = 1
(x/4)(3/3)+(x/6)(2/2)
3x/12+2x/12=5x/12
5x/5=12/5
12/5 = 2.4
2.4 = 2hr.40 min B.
Joe can replace his brakes on his car in 1 hour. Steve can change the oil, rotate the tires and replace his brakes on his car in 2 hours. How long would it take them if they were to do it together as a team?
Rational equations can be used to get a general idea about the rate at which a job can be completed. This can be really useful for business owners and other areas of daily life.
Here is an example:
Scenario: Sue can paint the garage in 4 hours and Joe has carpal tunnel so he is slower and can paint the same garage in 6 hours. How long (number of hours) will it take Sue and Joe to paint the garage if they work together?
Solution: Sue can paint of the garage in 1 hour. Joe can paint of the garage in one hour. We don’t know how long it will take them working together, so we let x = the number of hours it takes them to paint the kitchen working together. Below is a table that relates the data from our problem. We are using the concept that (rate)(time) = fraction of the task done.
Now we can write an equation to represent: Fraction of work done by Sue in x hours + Fraction of work done by Joe in x hours = 1 job completed For your initial response:
Complete both parts.
a) Solve the rational equation in the example above. Make sure you label your answer properly and show your work.
b) Create a scenario similar to the example above and include the equation you would use to answer the question in your scenario. Ask your classmates to solve the equation. Make sure to check back at the end of the week to verify the answer to your equation!.
A. x/4 + x/6 = 1
(x/4)(3/3)+(x/6)(2/2)
3x/12+2x/12=5x/12
5x/5=12/5
12/5 = 2.4
2.4 = 2hr.40 min B.
Joe can replace his brakes on his car in 1 hour. Steve can change the oil, rotate the tires and replace his brakes on his car in 2 hours. How long would it take them if they were to do it together as a team?