Question

Carla is collecting rainwater in a barrel. Currently she has 18 inches of water in the barrel. The rain is falling at the rate of 1.5 inches per hour. How many hours would it take to collect 30 inches of rain in the barrel

Answer 1

Answer: it will take 9 hours.

Step-by-step explanation:

The rain is falling at the rate of 1.5 inches per hour. This means that the height of water in the barrel is increasing in arithmetic progression.

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + d(n - 1)

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 18 inches

d = 1.5 inches

The expression becomes

Tn = 18 + 1.5(n - 1)

For the number of hours it would take to collect 30 inches of rain in the barrel, Tn = 30

Therefore,

30 = 18 + 1.5(n - 1)

1.5(n - 1) = 30 - 18

1.5(n - 1) = 12

n - 1 = 12/1.5 = 8

n = 8 + 1

n = 9