1. Extraneous Solutions
and
Work Problems

2. Watch out for extraneous solutions!
Solve:
6 𝑥−3 = 8 𝑥 2 𝑥 2 −9 − 4𝑥 𝑥+3
Watch out for extraneous solutions!

3. Solve:
𝑥 𝑥−2 + 2 𝑥−4 = 4𝑥−12 𝑥 2 −6𝑥+8
𝐍𝐨 𝐬𝐨𝐥𝐮𝐭𝐢𝐨𝐧:𝐛𝐨𝐭𝐡 𝒙=𝟐 𝐚𝐧𝐝 𝒙=𝟒 𝐚𝐫𝐞 𝐞𝐱𝐭𝐫𝐚𝐧𝐞𝐨𝐮𝐬 𝐬𝐨𝐥𝐮𝐭𝐢𝐨𝐧𝐬

4. Paul can complete an inventory for his job in 2 hours
Paul can complete an inventory for his job in 2 hours. Alicia can complete the same inventory in 3 hours. How long will they take to complete the same inventory if they work together?
𝟏.𝟐 𝐡𝐨𝐮𝐫𝐬 𝐨𝐫 𝟏 𝐡𝐨𝐮𝐫 𝐚𝐧𝐝 𝟏𝟐 𝐦𝐢𝐧𝐮𝐭𝐞𝐬

5. Adam takes 30 minutes more than Kyra to clean the garage
Adam takes 30 minutes more than Kyra to clean the garage. Last time they worked together and it took them 20 minutes to finish the cleaning. How long would each of them take working by themselves?
𝐀𝐝𝐚𝐦 𝐰𝐨𝐮𝐥𝐝 𝐭𝐚𝐤𝐞 𝟔𝟎 𝐦𝐢𝐧𝐮𝐭𝐞𝐬
𝐊𝐲𝐫𝐚 𝐰𝐨𝐮𝐥𝐝 𝐭𝐚𝐤𝐞 𝟑𝟎 𝐦𝐢𝐧𝐮𝐭𝐞𝐬

6. One garden hose can fill a small above-ground swimming pool in 10 hours. A second larger hose can fill the pool twice as fast as the first one. If both hoses are used to fill the pool, how many hours will it take?
𝟔 𝟐 𝟑 𝐡𝐨𝐮𝐫𝐬 𝐨𝐫
𝟔 𝐡𝐨𝐮𝐫 𝐚𝐧𝐝 𝟒𝟎 𝐦𝐢𝐧𝐮𝐭𝐞𝐬