Problem Solving: Real-life Rational Equations

Problem Solving: Solve the following real-life rational equations, showing all necessary steps and calculations.

Problem 1: Two People Painting a House
Alice can paint a house alone in 10 hours, while Bob can do it in 15 hours. How long will it take them to paint the house together?

• 6 hours

• 8 hours

• 12.5 hours

• 25 hours

Problem Solving: Solve the following real-life rational equations, showing all necessary steps and calculations.

Anna walks at 4 mph and bikes at 12 mph. If she travels 30 miles total and spends the same amount of time walking as biking, how far did she walk?

• 6 miles

• 8 miles

• 10 miles

• 12 miles

Problem Solving: Solve the following real-life rational equations, showing all necessary steps and calculations.

Problem 3: Fuel Efficiency
A car gets 20 mpg in the city and 30 mpg on the highway. If it travels 500 miles total and uses 20 gallons of fuel, how many miles were driven on the highway?

• 200 miles

• 250 miles

• 300 miles

• 350 miles

Problem 4: Travel Time A cyclist travels 20 miles. He rides half the distance at 10 mph and the other half at 20 mph. What is his average speed for the entire trip?

• 13.33 mph

• 15 mph

• 12 mph

• 16 mph

Problem Solving: Solve the following real-life rational equations, showing all necessary steps and calculations.

Problem 5: Filling a Pool with a Leak
A pool can be filled by a pipe in 5 hours, but there is a small leak that empties it in 15 hours. If the pipe is left open and the leak is not fixed, how long will it take to fill the pool?

• 6 hours

• 7.5 hours

• 7 hours

• 5 hours

Problem Solving: Solve the following real-life rational equations, showing all necessary steps and calculations.

Anna walks at 4 mph and bikes at 12 mph. If she travels 30 miles total and spends the same amount of time walking as biking, how far did she walk?

• 6 miles

• 8 miles

• 10 miles

• 12 miles

A cyclist travels 30 miles. He rides half the distance at 15 mph and the other half at 30 mph. What is his average speed for the entire trip?

• 20 mph

• 22.5 mph

• 18 mph

• 25 mph

A car gets 20 mpg in the city and 30 mpg on the highway. If it travels 500 miles total and uses 20 gallons of fuel, how many miles were driven on the highway?

• 200 miles

• 250 miles

• 300 miles

• 350 miles

A cyclist travels 20 miles. He rides half the distance at 10 mph and the other half at 20 mph. What is his average speed for the entire trip?

• 13.33 mph

• 15 mph

• 12 mph

• 16 mph

A car travels 120 miles on 4 gallons of fuel. Find the fuel efficiency in miles per gallon (mpg).

• 20 mpg

• 30 mpg

• 40 mpg

• 15 mpg