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Math  /  Algebra

Question11. The weather channel reported overnight rainfall of 1.5 inches and an average of 0.5 inches each hour for the remainder of the day. After how many hours will there be more than 5 inches of rain?
Inequality: \qquad
Solution: \qquad

Studdy Solution

STEP 1

1. Initial rainfall overnight is 1.5 inches.
2. Rainfall continues at a rate of 0.5 inches per hour during the day.
3. We need to find the number of hours after which the total rainfall exceeds 5 inches.

STEP 2

1. Define variables and set up the inequality.
2. Solve the inequality for the number of hours.

STEP 3

Define a variable for the number of hours of rainfall during the day. Let h h be the number of hours.

STEP 4

Set up the inequality to represent the total rainfall exceeding 5 inches.
The total rainfall is the sum of the overnight rainfall and the rainfall during the day:
1.5+0.5h>5 1.5 + 0.5h > 5

STEP 5

Solve the inequality for h h .
Subtract 1.5 from both sides:
0.5h>5−1.5 0.5h > 5 - 1.5 0.5h>3.5 0.5h > 3.5

STEP 6

Divide both sides by 0.5 to isolate h h :
h>3.50.5 h > \frac{3.5}{0.5} h>7 h > 7
The number of hours after which there will be more than 5 inches of rain is:
7 \boxed{7}

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