Answer:
44 hours
Step-by-step explanation:
Topic of this question: Creating and Solving Equations, Rates, and Proportions
Method 1: Creating and Solving Equations
Step 1: Find the amount drilled per hour
To do this, we have to divide the amount drilled by the number of hours it took to drill and find how much is being drilled per hour.
(I know it's a mouthful)
-72ft = 24x, where x is the amount drilled per hour
-72ft ÷ 24 = x
-3ft = x
-3ft per hour
Step 2: Find how many hours it takes to drill to -132 ft
Since we know the rate of drilling per hour, we can divide the target amount by the amount drilled per hour
-132 ÷ -3 = y, where y is the number of hours it takes
44 = y
y = 44
It will take a total of 44 hours to drill to -132 ft
Method 2: Proportions
We can set up a proportion like this, where we know that it takes 24 hours to drill 72 ft, but we don't know how long it takes to drill 132 feet
[tex]\frac{-72}{24} = \frac{-132}x[/tex]
Cross multiply
[tex]-72x = 24 * -132[/tex]
Simplify
[tex]-72x = -3168\\[/tex]
Divide both sides by -72
[tex]x = -3,168/-72[/tex]
[tex]x = 44[/tex]
It will take a total of 44 hours to dig to -132 ft
-Chetan K
