# College Algebra: Systems of Equations Application Word Problems (8 Problems)

22. Speed of a Plane: Two planes leave Low Angeles at the same time. One heads south to San Diego; the other heads north to San Francisco. The San Francisco plane flies 50 mph faster. In 1/2 hour, the planes are 275 miles apart. What are their speeds?

28. Wind Speed: Joe traveled against the wind in a small plane for 3 hr. The return trip with the wind took 2.8 hours. Find the speed of the wind if the speed of the plane in still air is 180 mph.

30. Painting a House: Repeat Exercise 29, but assume that Joe takes 6 hr working alone, and Same take 8 hrs working alone. (29. If Joe can paint a house in 3 hr and Sam can paint the same house in 5 hr, how long does it take them to do it together?)

32. Filling a Settling Pond: A sewage treatment plant has two inlet pipes to its settling pond. One can fill the pond in 10 hr, the other in 12 hr. If the first pipe is open for 5 hr and then the second pipe is opened, how long will it take to fill the pond?

38. Acid Mixture: travis Hayes needs 10% hydrochloric acid for a chemistry experiment. How much 5% acid should be mixed with 60 mL of 20% acid to get a 10% solution?

40. Acid Mixture: How much pure acid should be added to 6L of 30% acid to increase the concentration to 50% acid?

42. Buying and Selling Land: Anoa bought two plots of land for a total of $120,000. When she sold the first plot, she made a profit of 15%. When she sold the second, she lost 10%. Her total profit was $5500. How much did she pay for each piece of land?

Cookbook Royalties: Latasha Williams earned $48,000 from royalties on her cookbook. She pai a 28% income tax on these royalties. The balance was invested in two ways, some of it at 3.25% interest and some at 1.75%. The investments produced $904.80 interest per year. Find the amount invested at each rate.

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#### Solution Summary

This solution provides the equations for eight systems of equations from the Word problems and solves them in an attached Word document.