Problem
Word problem on area Involving conversions between systems A farmer has farmland that is a rectangle $4 \mathrm{~km}$ long and $2.5 \mathrm{~km}$ wide. He wants to completely cover the farmland in dirt. He knows the area each truckload of dirt covers, but only in square miles. (a) Find the area of the farmland in square miles. Do not round intermediate computations and round your final answer to two decimal places. Use the table of conversion facts, as needed. mi (b) The farmer wants to cover his farmland with dirt. He doesn't have any to begin with and he can't buy partial truckloads of dirt. Each truckload of dirt covers 0.9 mi $^{2}$. How many whole truckloads of dirt does the farmer need to buy to completely cover his farmland? truckloads (c) If each truckload of dirt costs $\$ 85.29$, how much will he need to spend on dirt? Write your answer to the nearest cent. Conversion facts for length \begin{aligned} 1 inch $(\mathrm{in}) & =2.54$ centimeters $(\mathrm{cm}) \\ 1$ foot $(\mathrm{ft}) & =30.48$ centimeters $(\mathrm{cm}) \\ 1$ yard $(\mathrm{yd}) & \approx 0.91$ meters $(\mathrm{m}) \\ 1$ mile $(\mathrm{mi}) & \approx 1.61$ kilometers $(\mathrm{km})\end{aligned}$ Note that $\approx$ means "is approximately equal For this problem, treat $\approx$ as if it were $=$. Explanation Check
Solution
Step 1 ：Given the length of the farmland is 4 km and the width is 2.5 km. We know that 1 mile is approximately equal to 1.61 kilometers.
Step 2 ：First, convert the length and width from kilometers to miles by dividing by 1.61. The length in miles is \( \frac{4}{1.61} \approx 2.48 \) miles and the width in miles is \( \frac{2.5}{1.61} \approx 1.55 \) miles.
Step 3 ：Then, calculate the area of the farmland in square miles by multiplying the length and width. The area in square miles is \( 2.48 \times 1.55 \approx 3.86 \) square miles.
Step 4 ：Final Answer: The area of the farmland in square miles is \( \boxed{3.86} \).
