Real-Life Problems

1. A faucet fills a tank in 5 hours, another in 3 hours. How long to fill together?
2. A chemist mixes solutions: 3L of 10% acid with 5L of 20% acid. Find final concentration.
3. Two cars start from the same point. One travels 60 mph, the other 45 mph. After how long will they be 75 miles apart?
4. Work problem: 4 people can paint a house in 6 days. How many days for 6 people?
5. Mixing problem: Combine 8% salt solution with 12% solution to get 10% concentration. How much of each?
6. Distance-rate-time: Train A 90 km/h, Train B 60 km/h, 150 km apart. When will they meet?
7. Financial problem: $1,200 invested at different rates for 2 years yields $180 interest. Find rates.
8. Speed problem: A boat goes downstream 30 km in 2 h, upstream same distance in 3 h. Find boat and current speed.
9. Proportion problem: Recipe calls for 2 cups sugar to 5 cups flour. How much sugar for 12 cups flour?
10. Mixture problem: Combine nuts worth $6/lb and $8/lb to get 10 lbs at $7/lb. Find amounts of each type.