Question

You are taking a test that contains 60 math problems. There is a time limit of 90 minutes in which to complete it. After doing 30 problems, you look at the clock and realize you must work twice as fast in order to complete the test in the allotted time. How many problems must you do per minute on the second half of the test in order to finish on time?

Answer 1

1 prob/min

you have 30 min left after it took you 60 min to do 1st 30 problems

Answer 2

If you wanted to show your work, you could write it out more...

let s = problems per min on first 30 questions, and let and t = time to finish first 30 questions. Then
\[s = \frac{ 30 }{ t }\]
For the 2nd 30 questions, the new speed is going to be 2s, and the time remaining is 90 minutes minus the time spent so far, t. So, for the 2nd 30 questions,
\[2s = \frac{ 30 }{ 90-t }\]
and 2s also equals 2 times the expression for s in the first 30 minute section,
\[2s = 2 (\frac{ 30 }{ t })\]
So
\[2s = \frac{ 30 }{ 90-t } = 2 (\frac{ 30 }{ t })\]
\[\frac{30}{90-t} = \frac{60}{t}\]
\[30t = 5400 - 60t\]
\[90t = 5400\]
t = 60
so time remaining for last 30 questions is 90-60=30, therefore you have to do one question per minute, twice as fast as you did the first 30 questions in 60 minutes.

@dumbcow had it right though :)

Answer 3

very nice