a teacher has 3 hours to grade all the papers submitted by the 35 students in her class. she gets through…

Explanation:

Step1: Calculate initial grading - rate

The teacher grades 5 papers in 30 minutes. So the initial rate $r_1=\frac{5}{30}=\frac{1}{6}$ papers per minute.

Step2: Calculate remaining time and papers

The teacher has 3 hours (3 * 60 = 180 minutes) in total. She has already spent 30 minutes, so the remaining time $t = 180 - 30=150$ minutes. The total number of papers is 35, and she has graded 5, so the remaining papers $n = 35 - 5 = 30$.

Step3: Calculate required grading - rate

The required rate $r_2$ to grade the remaining 30 papers in 150 minutes is $r_2=\frac{30}{150}=\frac{1}{5}$ papers per minute.

Step4: Calculate the percentage increase in speed

The formula for percentage increase in speed is $\text{Percentage increase}=\frac{r_2 - r_1}{r_1}\times100%$. Substitute $r_1=\frac{1}{6}$ and $r_2=\frac{1}{5}$ into the formula: [ \begin{align*} \frac{\frac{1}{5}-\frac{1}{6}}{\frac{1}{6}}\times100%&=\frac{\frac{6 - 5}{30}}{\frac{1}{6}}\times100%\ &=\frac{\frac{1}{30}}{\frac{1}{6}}\times100%\ &=\frac{1}{30}\times6\times100%\ & = 20% \end{align*} ]

Answer:

20%