Grade 12 Rational Equations Word Problems

Rational Equations Word Problems

Read each word problem carefully, set up a rational equation, and solve for the unknown. Show all your work.

1. John can paint a house in 6 days. Mark can paint the same house in 4 days. If they work together, how many days will it take them to paint the house?

2. A large pipe can fill a tank in 8 hours. A smaller pipe can fill the same tank in 12 hours. If both pipes are opened simultaneously, how long will it take to fill the tank?

3. A boat travels 60 miles upstream in the same amount of time it travels 90 miles downstream. If the speed of the current is 5 mph, what is the speed of the boat in still water?

4. An airplane flies 800 miles with a tailwind of 30 mph in the same time it flies 680 miles against the same wind. What is the speed of the airplane in still air?

5. The ratio of boys to girls in a class is 3:2. If there are 15 boys, how many girls are there?

6. A recipe calls for 2 cups of flour for every 3 cups of sugar. If you use 5 cups of flour, how much sugar do you need?

7. When solving rational equations, the first step is often to find a   to clear the denominators.

8. It is crucial to check for   solutions, which are values that make the denominator zero.