Consider the scenario.
Special equipment is used at a job site to dig holes. A hole is dug to a depth of 1.2 feet when the special drilling device hits rock. The progress slows to just 34
feet per hour of digging. The hole must be dug to a depth of at least 1212
feet today to stay on schedule.
Let d = the number of hours required.
What is the minimum number of hours the drill must continue at its present rate to accomplish the task?
Represent the scenario with an inequality, and solve the inequality.
What is the solution?
The drilling progress slows down to 34 feet per hour after it hits rock. So, for the hole to reach a depth of at least 1212 feet, we can write the inequality:
1.2 + 34d ≥ 1212
To solve this inequality, we can subtract 1.2 from both sides:
34d ≥ 1212 - 1.2
34d ≥ 1210.8
Now, divide both sides by 34:
d ≥ 1210.8 / 34
d ≥ 35.6
Since the number of hours must be a whole number, the minimum number of hours the drill must continue at its present rate is 36 hours.