Question

you work at a manufacturing plant. you need to fill 4 rectangular vats that are each 12 feet long, 8 feet wide, and 5 feet high with a chemical solvent. the pump you are using fills at the rate of 0.8 cubic feet per second. at this rate, how many minutes will it take to fill the 4 vats?
a. 6
b. 10
c. 26
d. 40
e. 1,536

Explanation:

Step1: Calculate volume of one vat

The volume $V$ of a rectangular - prism (vat) is given by $V = l\times w\times h$, where $l = 12$ feet, $w = 8$ feet, and $h = 5$ feet. So, $V=12\times8\times5=480$ cubic feet.

Step2: Calculate volume of 4 vats

Since there are 4 vats, the total volume $V_{total}$ is $V_{total}=4\times480 = 1920$ cubic feet.

Step3: Calculate time in seconds

The pump fills at a rate of $r = 0.8$ cubic feet per second. Using the formula $t=\frac{V}{r}$, where $V = V_{total}=1920$ cubic feet and $r = 0.8$ cubic feet per second, we get $t=\frac{1920}{0.8}=2400$ seconds.

Step4: Convert seconds to minutes

Since there are 60 seconds in a minute, the time $T$ in minutes is $T=\frac{2400}{60}=40$ minutes.

Answer:

D. 40