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.

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.