Question

What is the constant of variation if: A teacher grades 25 students essays in 4 hours. Assuming he grades at the same speed, how long will it take him to grade 35 essays?

The constant of variation should be a ratio, and the quantities vary directly.

Answer 1

9 tests per hour

Explanation:

If it's quantities are directly, 27/3=9

The constant variation is 9.

Answer 2

Direct Variation:

y = kx where k is the constant of variation

Number of essays: y
Number of hours: x

25 = k(4)
k = 25/4 ⇒ constant of variation

Find the number of hours (x) to grade 35 essays (y):

y = kx
35 = (25/4)(x)
x = (35)((4/25)
x = 140/25
x = 5 ³/₅ hours
(³/₅) (60 minutes) = 36 minutes
x = 5 hours and 36 minutes

Divide 25/4 to figure out how many essays the teacher grades in 1 hour.

It would take 5.36 hours.