Mastering Rational Equations: Real-Life Challenges

A car travels at a speed of 60 miles per hour. How long will it take to travel 180 miles? Write a rational equation to represent this situation and solve for time.

• 3 hours

• 5 hours

• 4 hours

• 2 hours

A recipe requires 3/4 cup of sugar for every 2 cups of flour. If you want to use 6 cups of flour, how much sugar do you need? Set up a rational equation and solve for the amount of sugar.

• 4.5 cups of sugar

• 1.5 cups of sugar

• 3 cups of sugar

• 2.25 cups of sugar

A tank can be filled by a pipe in 4 hours and emptied by another pipe in 6 hours. If both pipes are open, how long will it take to fill the tank? Create a rational equation to find the time needed to fill the tank.

• 10 hours

• 14 hours

• 12 hours

• 8 hours

A cyclist travels 12 miles in 1.5 hours. If the cyclist increases their speed by 4 miles per hour, how long will it take to travel 24 miles? Formulate a rational equation and solve for the new time.

• 2 hours

• 4 hours

• 1 hour

• 3 hours

A swimming pool can be filled by one hose in 5 hours and drained by another hose in 8 hours. If both hoses are used simultaneously, how long will it take to fill the pool? Write a rational equation and solve for the time.

• 15 hours

• 13.33 hours

• 12 hours

• 10 hours

A store sells pencils at $0.50 each and erasers at $0.75 each. If a student buys a total of 10 items and spends $6.00, how many of each item did they buy? Set up a rational equation to solve for the number of pencils and erasers.

• 4 pencils and 6 erasers

• 7 pencils and 3 erasers

• 6 pencils and 4 erasers

• 5 pencils and 5 erasers

A water tank is filled at a rate of 3 gallons per minute. If it takes 20 minutes to fill the tank, how many gallons does the tank hold? Create a rational equation to find the capacity of the tank.

• 45 gallons

• 60 gallons

• 30 gallons

• 75 gallons

A train travels 150 miles in 2.5 hours. If it continues at the same speed, how far will it travel in 4 hours? Write a rational equation to determine the distance traveled in that time.

• 180 miles

• 300 miles

• 240 miles

• 200 miles

A gardener can plant a row of flowers in 3 hours. If they work with a friend who can plant the same row in 2 hours, how long will it take them to plant the row together? Formulate a rational equation and solve for the combined time.

• 1.2 hours

• 3.5 hours

• 1 hour

• 2.5 hours

A factory produces 500 widgets in 10 hours. If the production rate increases by 50 widgets per hour, how long will it take to produce 1000 widgets? Set up a rational equation to find the new production time.

• 15 hours

• 10 hours

• 12 hours

• 8 hours