QuestionAn oil spill spreads 25 m² every $\frac{1}{6}$ hour. What is the total area after 2 hours?

Studdy Solution

STEP 1

Assumptions1. The oil spill spreads at a constant rate of25 square meters every $\frac{1}{6}$ hour. . We are asked to find the area of the oil spill after hours.

STEP 2

First, we need to find out how many $\frac{1}{6}$ hour intervals are there in2 hours. We can do this by dividing the total time by the time interval.
$Number\, of\, intervals = Total\, time / Time\, interval$

STEP 3

Now, plug in the given values for the total time and time interval to calculate the number of intervals.
$Number\, of\, intervals =2 / \frac{1}{6}$

STEP 4

Calculate the number of intervals.
$Number\, of\, intervals =2 / \frac{1}{6} =12$

STEP 5

Now that we have the number of intervals, we can find the total area of the oil spill. This can be done by multiplying the area spread in each interval by the number of intervals.
$Total\, area = Area\, per\, interval \\times Number\, of\, intervals$

STEP 6

Plug in the values for the area per interval and the number of intervals to calculate the total area.
$Total\, area =25 \\times12$

STEP 7

Calculate the total area of the oil spill.
$Total\, area =25 \\times12 =300\, square\, meters$ The area of the oil spill after2 hours is300 square meters.

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