Question

In digging a hole, the construction crew records the depth of the hole relative to the ground level. The starting depth is zero feet. The table shows the proportional relationship between the depth of the hole and the number of hours digging. Find the constant of proportionality. How many hours of digging does it take for the depth of the hole to reach −35.75 feet?

Answer 1

Digging a hole

We want to know how hepth is the hole after one work hour.

From the two first lines we can see that they dig a hole from -8.25 to -13.75, then

Δdepth = depth₂ - depth₁ = -13.75 +8.25= -5.5 feet in two hours

Then if we dive we will have the depth each hour

-5.5/2 = -2.75 depth each hour

Constant of proportionality: -2.75

We want to know how many hours correspond to reach -35.75 feet. In order to do so, we divide it by the depth they reach each hour:

-35.75/-2.75 = 13 hours

Answer: it takes 13 hours of digging