# Algebraic Word Problems Worksheet

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1. If it takes one person one hour to bake one cake, how long does it take ten people to bake ten cakes?
2. If an alloy containing 30% silver is mixed with a 55% silver alloy to get 800 pounds of 40% alloy, how much of each must be used?
3. Felicia left Rome at 8 am and drove her Ferrari at 80 mph from Rome to Sorrento. She then took the boat to Capri for the day, returning to Sorrento 5 hours later. On the return trip from Sorrento to Rome she averaged 60 mph and arrived in Rome at 8 pm. How far is it from Rome to Sorrento?
4. A pharmacist has to fill a prescription calling for 5 ounces of a 12% argyrol solution. She has 5 ounces of a 15% solution and 5 ounces of a 5% solution. If she starts with the 5 ounces of 15%, how much must she draw off and replace with 5% in order to fill the prescription?
5. John walks east at a certain rate. Sue starts at the same time from the same place as John and walks south at a rate k times as fast as John's rate. Sue turns and walks directly northeast but John continues to walk east. If Sue eventually meets John, what is the value of k? (Hint: Draw a diagram.)
6. Mr. Caleb hires Jay and Debbie to prune his vineyard. Jay can prune the vineyard in 50 hours and Debbie can prune it in 40 hours. Assuming they work at these rates, how many hours will it take them working together?
7. Alfie, Beth, and Gemma are hired to paint signs. In 8 hours Alfie can paint 1 sign, Beth can paint 2 signs, and Gemma can paint 1 1/3 signs. They all come to work the first day, but Gemma doesn't like the job and quits after 3 hours. Beth works half an hour longer than Gemma and quits. How long will it take Alfie to finish the 2 signs they were supposed to paint?