If three teachers can grade 40 tests in 3 hours, how many hours will it take 12 teachers to grade 480 tests?
Each test is graded in
R=(3 teachers * 3 hours)/ 40 tesets
=9/40 teacher-hour/test
480 tests will require
Time=480 tests *R
=480* (9/40) tests*teacher-hours/test
=108 teacher-hours.
12 teachers will take
Time = 108 teacher-hours / 12 teachers
=108/12 hours
=9 hours.
To solve this problem, we can set up a proportion using the number of tests and the number of teachers.
First, let's find the number of tests that one teacher can grade in 1 hour. Since three teachers can grade 40 tests in 3 hours, one teacher can grade (40 tests / 3 hours) = 13.33 tests in 1 hour (rounded to the nearest whole number).
Next, let's find how many hours it takes one teacher to grade 480 tests. Since one teacher can grade 13.33 tests in 1 hour, it will take one teacher (480 tests / 13.33 tests per hour) = 36 hours (rounded to the nearest whole number).
Finally, to find how many hours it will take 12 teachers, we can set up a proportion:
1 teacher : 36 hours :: 12 teachers : x hours
Cross multiplying, we get:
(1 teacher)(x hours) = (12 teachers)(36 hours)
x hours = 12 * 36 hours
x hours = 432 hours
Therefore, it will take 12 teachers to grade 480 tests in 432 hours.
To find the answer, we need to determine the rate at which the teachers grade the tests and then use that rate to calculate the time it takes for 12 teachers to grade 480 tests.
Let's start by finding the rate at which three teachers grade tests. We know that they can grade 40 tests in 3 hours. To get the rate, we divide the number of tests by the number of hours:
Rate = Number of tests / Number of hours
Rate = 40 tests / 3 hours
Rate = 40/3 tests/hour
Now, we can use this rate to calculate the time it takes for 12 teachers to grade 480 tests.
Number of tests = Rate × Number of hours
480 tests = (40/3) tests/hour × Number of hours
To find the number of hours, we rearrange the equation:
Number of hours = 480 tests / (40/3) tests/hour
Number of hours = 480 tests × (3/40) hour/test
Now, we can calculate the number of hours:
Number of hours = (480 × 3) / 40
Number of hours = 36 hours
Therefore, it will take 12 teachers 36 hours to grade 480 tests.