Question

The gallons of way used to take a shower varies directly with the number of minutes in the shower .If a 6 minute shower uses 36 gallons of water, find the constant of variation

Answer 1

constant of variation (k) = 6

Explanation:

Let us first represent the sentence in direct variation expression:

"the gallons of water used to take a shower varies directly with the number of minutes in the shower"

Let the gallons of water used = g

Let the number of minutes spent in the shower = m

g ∝ m

where: ∝ = sign of proportionality

This means that as g increases, m increases also, and the same holds for decrease too.

g ∝ m

g = km

where k = constant of variation ( or proportionality constant)

Next, If a 6-minute shower uses 36 gallons of water, find the constant of variation

g = 36 gallons

m = 6 minutes

∴ g = km

= 36 = k × 6

k = 36 ÷ 6 = 6

k = 6