Rate problems

Question

can anybody tell me why my approach to  the following question in this way is wrong?

Q. 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? 

 

my answer: cur working rate is 1/6

requmired working rate is 1/5 

so ((1/5-1/6)*100)/1/6 =20% 

but the answer is wrong. Can anybody tell me why this method is incorrect? 

Answer 1

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

 

Looks like no error on your part.  I suspect the study guide is in error.  It will not be the first time, or the last.

 

 

Answer 2

Yes, her first rate is 1 paper per 6 minutes.

She must grade 30 papers in 150 minutes, that is 1 paper per 5 minutes.

Get a common denominator:

At first 10 papers per hour

Afterwards 12 papers per hour

She must work 2 papers per hour faster

So that is 2/10, 0.2, 20%.

Look's like mine is wrong also.