Simplifying Rational Functions in Real-Life Scenarios

A car travels a distance of 120 miles at a speed of x miles per hour. Write a rational function to represent the time taken to travel this distance. What is the simplified form of the function?

• T(x) = 120 * x

• T(x) = 120 + x

• T(x) = x / 120

• T(x) = 120 / x

A recipe requires 3/4 cup of sugar for every 2 cups of flour. Write a rational expression for the amount of sugar needed per cup of flour and simplify it.

• 3/8

• 1/2

• 2/3

• 1/4

A tank can be filled by two pipes. Pipe A fills the tank in 4 hours, while Pipe B fills it in 6 hours. Write a rational function to represent the rate at which the tank fills when both pipes are open. Simplify the function.

• 5/12

• 3/8

• 1/2

• 2/3

A company produces x units of a product and incurs a cost of C(x) = 500/x + 200 dollars. Identify the rational function and simplify it to find the average cost per unit produced.

• A(x) = 500/x + 200/x^2

• A(x) = 500/x^2 + 200

• A(x) = 500/x^2 + 200/x

• A(x) = 200/x + 500/x^2

A cyclist travels at a speed of 15 miles per hour. Write a rational function to express the distance traveled in terms of time. Simplify the function to find the distance per hour.

• 20 miles per hour

• 15 miles per hour

• 10 miles per hour

• 25 miles per hour

A rectangular garden has a length of (x + 5) meters and a width of (x - 3) meters. Write a rational expression for the area of the garden and simplify it.

• x^2 + 2x - 15

• x^2 - 2x + 15

• x^2 - 5x + 15

• x^2 + 8x - 15

A swimming pool can be drained in 8 hours. If the pool is currently full, write a rational function to represent the volume of water left in the pool after t hours. Simplify the function.

• V(t/8)

• V(8 - t)

• V(8t)

• V(1 - t/8)

A store sells x items for $20 each. Write a rational function to represent the total revenue R(x) from selling x items. Simplify the function to find the revenue per item sold.

• 20

• $15

• $25

• $10

A car's fuel efficiency is represented by the function E(x) = 30/(x + 2) miles per gallon, where x is the number of passengers. Identify the rational function and simplify it to find the efficiency per passenger.

• E(x) = 30/(x - 2) miles per gallon

• E(x) = 30/(x + 2) miles per gallon

• E(x) = 15/(x + 2) miles per gallon

• E(x) = 30x/(x + 2) miles per gallon

A farmer has a field that is 100 acres. If he plants x acres of corn, write a rational function to represent the remaining acres for other crops. Simplify the function to find the remaining area.

• 50 - x

• 100 - x

• x - 100

• 100 + x