Question

A teacher has 3 hours to grade all the papers submitted by the 35 students in her class. She gets through the first 5 papers in 30 minutes. How much faster does she have to work to grade the remaining papers in the allotted time?

Answer 1

So, she has 3hrs to grade all papers, for 35 students.. alrite.

the first 5, she does them in 30minutes.. what's the speed rate? well, 5/30 or 1/6

now, she has still 2 hours and a half, or 150 minutes, to do the remaining 30 papers... she has to work at a rate of 30/150 then... which is 1/5 simplified.

now if we take 1/6 as the 100%, what is 1/5 in percentage then?

$\bf \begin{array}{ccllll} rate&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{1}{6}&100\\\\ \frac{1}{5}&x \end{array}\implies \cfrac{\frac{1}{6}}{\frac{1}{5}}=\cfrac{100}{x}\implies \cfrac{1}{6}\cdot \cfrac{5}{1}=\cfrac{100}{x}\implies \cfrac{5}{6}=\cfrac{100}{x} \\\\\\ x=\cfrac{6\cdot 100}{5}\implies x=120$

so 1/5 is 120% in relation to 1/6... meaning the rate of 1/5 she needs to move through, namely 1 paper every 5 minutes, is 20% faster than 1/6.

Answer 2

At first, she was grading papers at 10 papers per hour. To meet her time limit, she would have to begin grading them at 12 papers per hour, or 20% faster than her previous rate