Answer :
Certainly! Let's find the average rate at which the water level changed every week in a step-by-step manner.
Step 1: Understand the Problem
The water level of a lake fell by [tex]\(1 \frac{1}{2}\)[/tex] inches over a period of [tex]\(1 \frac{2}{3}\)[/tex] weeks. We need to find the average rate at which the water level changed every week.
Step 2: Convert Mixed Numbers to Fractions
First, we convert the mixed numbers to improper fractions to make calculations easier.
- The water level fell [tex]\(1 \frac{1}{2}\)[/tex] inches. In improper fraction form, this is:
[tex]\[
1 \frac{1}{2} = \frac{3}{2}
\][/tex]
- The duration of the dry spell was [tex]\(1 \frac{2}{3}\)[/tex] weeks. In improper fraction form, this is:
[tex]\[
1 \frac{2}{3} = \frac{5}{3}
\][/tex]
Step 3: Calculate the Average Rate
The average rate of change is found by dividing the total fall in water level by the total number of weeks:
[tex]\[
\text{Average rate} = \frac{\frac{3}{2}}{\frac{5}{3}}
\][/tex]
To divide fractions, multiply by the reciprocal of the divisor:
[tex]\[
\frac{3}{2} \times \frac{3}{5} = \frac{3 \times 3}{2 \times 5} = \frac{9}{10}
\][/tex]
So, the average rate of change every week is [tex]\(\frac{9}{10}\)[/tex] inches.
Conclusion
The average rate at which the water level changed every week is [tex]\(\frac{9}{10}\)[/tex] inches.
Step 1: Understand the Problem
The water level of a lake fell by [tex]\(1 \frac{1}{2}\)[/tex] inches over a period of [tex]\(1 \frac{2}{3}\)[/tex] weeks. We need to find the average rate at which the water level changed every week.
Step 2: Convert Mixed Numbers to Fractions
First, we convert the mixed numbers to improper fractions to make calculations easier.
- The water level fell [tex]\(1 \frac{1}{2}\)[/tex] inches. In improper fraction form, this is:
[tex]\[
1 \frac{1}{2} = \frac{3}{2}
\][/tex]
- The duration of the dry spell was [tex]\(1 \frac{2}{3}\)[/tex] weeks. In improper fraction form, this is:
[tex]\[
1 \frac{2}{3} = \frac{5}{3}
\][/tex]
Step 3: Calculate the Average Rate
The average rate of change is found by dividing the total fall in water level by the total number of weeks:
[tex]\[
\text{Average rate} = \frac{\frac{3}{2}}{\frac{5}{3}}
\][/tex]
To divide fractions, multiply by the reciprocal of the divisor:
[tex]\[
\frac{3}{2} \times \frac{3}{5} = \frac{3 \times 3}{2 \times 5} = \frac{9}{10}
\][/tex]
So, the average rate of change every week is [tex]\(\frac{9}{10}\)[/tex] inches.
Conclusion
The average rate at which the water level changed every week is [tex]\(\frac{9}{10}\)[/tex] inches.
