The water level of a lake fell by 1 1/2
inches during a 1 2/3
-week-long dry spell. Find the average rate at which the water level changed every week.
To find the average rate at which the water level changed every week, we need to divide the total change in water level by the number of weeks.
The total change in water level is 1 1/2 inches.
The number of weeks is 1 2/3 weeks.
To convert 1 2/3 weeks to an improper fraction, we multiply the whole number (1) by the denominator of the fraction (3), and add the numerator (2) to get 5. The new numerator is 5, and the denominator stays the same, 3. So, 1 2/3 as an improper fraction is 5/3.
Now, we can divide the total change in water level (1 1/2 inches) by the number of weeks (5/3).
1 1/2 ÷ 5/3 can be rewritten as (3/2) ÷ (5/3).
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
(3/2) ÷ (5/3) = (3/2) * (3/5)
Multiplying the numerators and denominators, we get 9/10.
Therefore, the average rate at which the water level changed every week is 9/10 inches per week.
To find the average rate at which the water level changed every week, we need to determine the total change in the water level and divide it by the number of weeks.
First, let's convert the time into weeks. Since the dry spell lasted for 1 2/3 weeks, we can express it as an improper fraction: (3/3 + 2/3) = 5/3
Next, we need to find the total change in the water level. The water level fell by 1 1/2 inches, which can be expressed as an improper fraction: (1/1 + 1/2) = 3/2
Now, we can calculate the average rate of change per week by dividing the total change by the length of time:
Average rate of change = Total change / Time
In this case, the total change is 3/2 inches and the time is 5/3 weeks:
Average rate of change = (3/2) inches / (5/3) weeks
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
Average rate of change = (3/2) * (3/5)
Multiplying fractions, we multiply the numerators together and the denominators together:
Average rate of change = (9/10) inches per week
Therefore, the average rate at which the water level changed every week during the dry spell is 9/10 inches per week.
To find the average rate at which the water level changed every week, we need to determine the total change in the water level over the given time period.
First, let's convert the time period of 1 2/3 weeks into a fraction. We can rewrite it as 5/3 weeks.
Next, we can calculate the total change in the water level by multiplying the rate of change per week by the number of weeks. In this case, the rate of change is 1 1/2 inches.
Total Change = Rate of Change x Number of Weeks
Total Change = (1 1/2 inches) x (5/3 weeks)
To make the calculation easier, let's first convert the mixed number 1 1/2 into an improper fraction:
1 1/2 = (2 * 1 + 1)/2 = 3/2
Now we can substitute the values into the equation:
Total Change = (3/2 inches) x (5/3 weeks)
When multiplying fractions, we can simply multiply the numerators and multiply the denominators to get the result:
Total Change = (3 * 5) / (2 * 3) = 15/6 inches
Finally, to find the average rate at which the water level changed every week, we divide the total change by the number of weeks:
Average Rate = Total Change / Number of Weeks
Average Rate = (15/6 inches) / (5/3 weeks)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
Average Rate = (15/6 inches) x (3/5 weeks)
Now we can simplify the expression:
Average Rate = (15 * 3)/(6 * 5) = 45/30 inches per week
To further simplify, we can reduce the fraction:
Average Rate = (3 * 3)/(2 * 5) = 9/10 inches per week
Therefore, the average rate at which the water level changed every week during the dry spell is 9/10 inches per week.