Answer: To find the average rate at which the water level changed every week, we need to simplify the complex fraction given.
The water level of the lake rose by one and two-thirds during a three and one-third week long wet spell.
To find the average rate of change per week, we can divide the total change in the water level by the number of weeks.
Let's start by converting the mixed numbers to improper fractions:
One and two-thirds can be written as 5/3.
Three and one-third can be written as 10/3.
Now, we can subtract the initial water level from the final water level:
(5/3) - 0 = 5/3.
Next, we divide the change in the water level by the duration of the wet spell:
(5/3) ÷ (10/3) = (5/3) × (3/10) = 5/10 = 1/2.
Therefore, the average rate at which the water level changed every week is 1/2. This means that, on average, the water level of the lake increased by half a unit every week during the wet spell.