1. 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?
Solution:
Total time available: 180 minutes
Time to grade first 5 papers: 30 minutes
Rate: R1 = 5/30 = 1/6 papers per minute
Time remaining to grade remaining papers:
180 – 30 = 150 minutes to grade 35 – 5 = 30 papers
Required rate to finish on time:
R2 = 30/150 = 1/5 papers per minute
How much bigger is R2 than R1?
R2/R1 = (1/5) / (1/6) = 6/5 = 1.2
R2 = 1.2 R1 ⇒ R2 is 20% greater then R1
Answer: 20% or 1
Short Cut Method:
He has been working at the rate of 10 papers per hour. She has 30 papers remaining and must grade them in the 2.5 hours that she has left, which corresponds to a rate of 12 papers per hour. of her previous rate, or 20% faster.
2. 24
3.
4. (4000 &5000)
5. 455
6. 88/7 (Not Sure)
7.10
Full Solution is ongoing…….Please stay……
