# 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?

Explanation

A teacher has 3 hours to grade all the papers submitted by the 35 students in her class.
3 hours is equal to $$3 \times 60=180$$ minutes.
She gets through the first 5 papers in 30 minutes. Therefore, the teacher evaluates at the speed of $$5 \times 2=10$$papers per hour as 1 hour is equal to 60 minutes.
The remaining time is 180−30=150 minutes.
The number of papers remaining is 35−5=30 .
The teacher has to evaluate 30 papers in 150 minutes to grade the remaining papers in the allotted time.
We try to find the number of papers she has to grade in 1 hour which is equal to 60 minutes.
So, she has to evaluate 30 papers in 150 minutes. This means she evaluates

30/150=1/5 papers in 1 minute. She has (1/5)*60 = 12 papers in 1 minute

The increase in number is 12−10=2 papers in 1 hour.

The percentage increase is $$(2 / 10) \times 100=20$$

She has to work 20% faster to grade the remaining papers in the allotted time.