Question

After raining for 34 of an hour, a rain gauge is 25 filled. If it continues to rain at that rate for 15 more minutes, what fraction of the rain gauge will be filled?

To help answer this question, Diego wrote the division equation 34÷25=?. Explain why this equation does not represent the situation.
Write a multiplication equation and a division equation that does represent the situation.

Answer 1

`\textbf{Fraction of gauge filled = }\bf(8)/(15)`

Explanation:

This equation does not represent the situation because to find the fraction of the rain gauge we need to : divide the fraction of gauge filled by the raining fraction of an hour

But, Diego wrote the incorrect division equation so, it does not represent the current situation.

Now, to find the required division and multiplication equations :

`(3)/(4)\text{ fraction of an hour = }(3)/(4)* 60=\text{ 45 minutes}\\\\\text{ Now, the rain continues to rain for 15 minutes more}\\\implies \text{The total raining time = 45 + 15 = 60 minutes}\\\\\text{So, we need to find the fraction of gauge filled in 60 minutes}\\\\\text{Fraction of gauge filled in 45 minute = }(2)/(5)\\\\\text{Fraction of gauge filled in 1 minute = }((2)/(5))/(45)=(2)/(5* 45)\\\\\text{Fraction of gauge filled in 60 minutes = }(2)/(5* 45)* 60=\bf(8)/(15)`

`\text{Division equation = }\frac{\text{fraction of gauge filled}}{\text{raining fraction of an hour}}\\\\\textbf{Division Equation : }((2)/(5))/((3)/(4))=(2)/(5)* (4)/(3)=(8)/(15)\\\\\text{Multiplication Equation = Fraction of gauge filled in 1 minute × 60}\\\\\textbf{Multiplicatiuon Equation : }(2)/(225)* 60=(8)/(15)`