Rates & Word Problems (Standard)

Multi-step exam-style items.

Phase 2 · ACT Math

Rates & Word Problems: core idea

Combined rates.

Two pumps fill a pool. One fills it in $6$ hours and the other in $3$ hours. What fraction of the pool do they fill in one hour together?

Hint: Add their hourly rates. Answer: 1/2.

1. A boat travels $30$ miles downstream in $2$ hours. The current is $3$ mph. Find the boat's still-water speed.
2. A store sells pens for $1.20$ and notebooks for $2.50$ . If $4$ pens and $3$ notebooks are bought, find the total.
3. A cyclist rides $15$ mph for $2$ hours, then $12$ mph for $3$ hours. What distance is covered?
4. A population of $8,000$ grows by $5\%$ annually. What is it after one year?
5. A $24$ -foot board is cut into pieces in ratio $2:3:7$ . Find the longest piece.
6. A worker completes $\frac38$ of a job Monday and $\frac14$ Tuesday. What fraction remains?
7. A $15,000$ dollar car loses $12\%$ of its value in one year. What is its value then?
8. A plane flies $480$ miles with a tailwind in $4$ hours. If wind speed is $20$ mph, find airspeed.
9. A $200$ dollar purchase has a $15\%$ coupon then $8\%$ sales tax. What is the final cost?