Question

A bathtub is draining at a constant rate. After 3 minutes, it holds 36 gallons of water. Seven minutes later, it holds 15 gallons of water. Write an equation the represents the number y of gallons in the tub after x minutes

Answer 1

y = 45 - 3x

Explanation:

Given that:

Bathtub drains at a constant rate :

Amount of water in tub after 3 minutes = 36 gallons

Amount of water in tub after 7 minutes later (3 + 7) ;(after 10 minutes) = 15 gallons

Using the slope - intercept relation:

y = mx + c

y = gallons in tub after x minutes

m = slope (rate at which water drains per minute)

C = intercept

Hence,

Amount of water in tub after 3 minutes = 36 gallons ; x = 3,; y = 36

Since water is draining gradient m is negative

36 = c - 3m - - - (1)

Amount of water in tub after 7 minutes later (3 + 7) ;(after 10 minutes) = 15 gallons

15 = c - 10m - - - (2)

Subtract (2) from (1)

21 = - 3m + 10m

21 = 7m

m = 3

From (1)

36 = c - 3(3)

36 = c - 9

36+ 9 = c

45 = c

Hence, the equation becomes ;

y = 45 - 3x