Question

In digging a hole, the construction crew at the Cecil County School of Technology records the location of the bottom of the hole relative to ground level.After 4 hours, the hole is 12.80 feet deep.Part A: What number represents the change in location, in feet, after 1 hour? Explain how you obtained your answer.Part B: If the crew were to continue digging at the same rate, what number would they record for the location, in feet, after 10 hours? Explain howyou obtained your answer.

Answer 1

Solution

- The rate at which the ground is dug is given to be 12.80 ft deep after 4 hours.

Part A:

- Thus, we can find the rate at which the depth changes as:

$\begin{gathered} Let\text{ the depth after 1 hour be }x \\ \frac{12.8ft}{4hours}=\frac{x}{1hour} \\ \\ \therefore x=\frac{12.8ft\times1hour}{4hours} \\ \\ x=3.2ft \end{gathered}$

- Therefore, the change in location per hour is 3.2ft after 1 hour

Part B:

- If the crew continue digging at the same rate for 10 hours, we simply multiply the rate at which they dig for 1 hour by 10.

- That is,

$\frac{3.2ft}{1hour}\times10hours=32ft$

- Thus, the location after 10 hours of digging is 32ft deep