Question

The mathcounts sprint round competition consists of 30 problems with a time limit of 40 minutes. suppose you complete 20 sprint round problems in 25 minutes. on average, how many times as long will you be able to spend on each remaining problem than you did on each of the first 20? express your answer as a common fraction.

Answer 1

6/5

Explanation:

The average time you spent per problem for the first 20 problems is 25/20 = 5/4 minutes. There are 40 - 25 = 15 minutes remaining, and 30 - 20 = 10 problems remaining, so the average time per remaining problem is 15/10 = 3/2 minutes. Hence, you can spend

(3/2)/(5/4) = 6/5

times longer on the remaining problems.

Answer 2

The number of remaining problems is:
30-20 = 10 problems.
The amount of time remaining is:
40-25 = 15minutes
For the first 20 problems the time per problem is:
t1 = 25/20 = 5/4 minutes
For the remaining problems the time per problem is:
t2 = 15/10 = 3/2 minutes
Answer:
you will be able to spend about 3/2 minutes on each remaining problem