Question: David can plant 300 flowers in the same time that it takes Sarah to plant 240.
David can also plant 10 more flowers each hour than Sarah can. If $D$ and $S$ are the respective rates (flowers per hour) that David and Sarah can plant, the equation that describes this relationship is $$\frac{300}{D} = \frac{240}{S}.$$
How many flowers can Sarah plant in an hour?
50 flowers
72 flowers
40 flowers
60 flowers
1. **State the problem:** We need to find Sarah's planting rate $S$ (flowers per hour) given that David plants 10 more flowers per hour than Sarah, and the times to plant 300 and 240 flowers are equal.
2. **Write the given equation:** $$\frac{300}{D} = \frac{240}{S}$$ where $D$ is David's rate and $S$ is Sarah's rate.
3. **Express David's rate in terms of Sarah's rate:** Since David plants 10 more flowers per hour, $$D = S + 10.$$
4. **Substitute $D$ into the equation:** $$\frac{300}{S + 10} = \frac{240}{S}.$$
5. **Cross multiply to solve for $S$: $$300 \times S = 240 \times (S + 10).$$**
6. **Expand the right side:** $$300S = 240S + 2400.$$
7. **Subtract $240S$ from both sides:** $$300S - 240S = 2400.$$
8. **Simplify:** $$60S = 2400.$$
9. **Divide both sides by 60:** $$\cancel{60}S = \frac{2400}{\cancel{60}}$$
10. **Calculate:** $$S = 40.$$
**Answer:** Sarah can plant **40 flowers per hour**.