Rational Equations Word Problems
Solve word problems involving rational equations, including distance, work, and mixture problems.
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Rational Equations Word Problems
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Read each word problem carefully, set up a rational equation, and solve for the unknown. Show all your work.
1. A boat travels 60 miles upstream in the same amount of time it travels 90 miles downstream. If the current's speed is 5 mph, what is the speed of the boat in still water?
2. John can paint a house in 10 hours. Mike can paint the same house in 15 hours. How long will it take them to paint the house if they work together?
3. A chemist has 20 liters of a 20% acid solution. How much pure acid should be added to make a 50% acid solution?
4. If it takes 3 hours for pipe A to fill a tank and 5 hours for pipe B to fill the same tank, which equation represents the time (t) it takes for both pipes to fill the tank together?
1/3 + 1/5 = t
1/3 + 1/5 = 1/t
3 + 5 = t
t/3 + t/5 = 1
5. When solving a rational equation, the first step is often to find a to clear the denominators.
6. A solution that makes any denominator in the original equation equal to zero is called an solution.