Exploring Rational Functions: Real-Life Applications & Solutions

A car travels a distance of 120 miles at a speed of x miles per hour. The time taken for the journey can be expressed as 120/x. If the car takes 2 hours to complete the journey, what is the speed of the car?

• 60 miles per hour

• 50 miles per hour

• 75 miles per hour

• 90 miles per hour

A tank can be filled by two pipes. Pipe A can fill the tank in 4 hours, while Pipe B can fill it in 6 hours. If both pipes are opened together, how long will it take to fill the tank?

• 5 hours

• 2.4 hours

• 1.5 hours

• 3 hours

The cost of producing x items is given by the function C(x) = 100/x + 50. What is the cost of producing 20 items?

• 45

• 55

• 60

• 70

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 54 square meters, find the dimensions of the garden using a rational equation.

• Width: 7 meters, Length: 10 meters

• Width: 5 meters, Length: 8 meters

• Width: 4 meters, Length: 7 meters

• Width: 6 meters, Length: 9 meters

A person can complete a job in 5 hours, while another can do it in 3 hours. If they work together, how long will it take them to finish the job?

• 4 hours

• 1.875 hours

• 2.5 hours

• 6 hours

The function f(x) = 1/(x-2) represents the height of a water tank as a function of time. What is the height of the water tank when x = 3?

• 1

• 0

• 2

• -1

A recipe requires 2/x cups of sugar for x servings. If you want to make 10 servings, how much sugar do you need?

• 0.5 cups

• 1 cup

• 2 cups

• 0.2 cups

A cyclist travels at a speed of 15 miles per hour. The distance d can be expressed as d = 15t, where t is the time in hours. If the cyclist travels for 2 hours, how far does he go?

• 45 miles

• 30 miles

• 60 miles

• 15 miles

The function g(x) = (3x + 6)/(x - 1) represents the profit from selling x items. What is the profit when 5 items are sold?

• 5.25

• 4.75

• 6.00

• 5.00

A pool can be drained by a pipe in 8 hours. If the pool is currently full, how long will it take to drain it if the pipe is opened?

• 4 hours

• 8 hours

• 12 hours

• 16 hours