Rates and Work (Medium)

AMC 10/12 mid (≈Q9–16) — multi-step.

Rates and Work: core idea

Combined rates.

Two workers finish a job in $6$ and $3$ hours alone. Find their combined time in hours.

Hint: Use reciprocal rates for combined-work questions. Answer: 2.

1. A car travels $120$ miles at $40$ mph and returns at $60$ mph. Find total travel time.
2. A $100$ item is discounted $20\%$ then $10\%$ . Find the final price.
3. One pipe fills a tank in $4$ hours and another in $6$ hours. Find their combined rate as a fraction.
4. A $200$ investment earns $5\%$ simple interest for $3$ years. Find the interest.
5. A boat travels $30$ miles downstream in $2$ hours with current $3$ mph. Find its still-water speed.
6. A mixture is $25\%$ salt. How much salt is in $40$ liters?
7. A $50$ price includes $8\%$ tax. Find the total.
8. A cyclist rides $18$ miles at $12$ mph and $12$ miles at $6$ mph. Find average speed.
9. A population of $500$ grows $10\%$ . Find the new population.