A drill can dig through rock at a rate of \( 2 \frac{1}{2} \) inches per hour. How many hours will it take for the drill to reach five feet below the rocky surface, assuming it maintains this rate of dizging? The solution is

To determine how long it will take the drill to reach five feet below the surface, first convert five feet to inches, knowing that there are 12 inches in a foot. So, \( 5 \text{ feet} = 5 \times 12 = 60 \text{ inches} \). Next, convert the drilling rate to an improper fraction. The rate \( 2 \frac{1}{2} \) inches per hour can be expressed as \( \frac{5}{2} \) inches per hour. Now, to find the total hours needed, divide the total distance by the rate: \[ \text{Time} = \frac{\text{Total Distance}}{\text{Rate}} = \frac{60}{\frac{5}{2}} = 60 \times \frac{2}{5} = 24 \text{ hours} \] So, it will take the drill 24 hours to reach five feet below the rocky surface. Drilling through rock has been a crucial part of human advancement. Think ancient civilizations using simple picks and hammers, and now we have powerful drills that can reach great depths. It's a symbol of how far technology has come—transforming hard labor into efficient processes. From mining to construction, the need for precision drilling is everywhere. Whether it's creating tunnels for trains or excavating for new skyscrapers, understanding drilling metrics can aid project management and ensure safety. So, knowing the rate at which materials can be drilled is essential for effective planning and execution in engineering and construction!