Question

From 7:00 AM to 11:00 AM it rained 2.25 inches. At 11:00 AM the rain increased to fall at a rate of 1.25 in. every two hours. How many inches of rain landed on the ground by 5:00 PM?

• A. 7
• B. 9.75
• C. 6
• D. 3.25
• E. 7.125

Hint:

For multi-step time and rate problems, always break the problem down into distinct time intervals. Calculate the value for each interval separately before combining them for the final answer.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem requires calculating the total rainfall by summing the rainfall from two distinct periods with different rates.
Step 2: Detailed Explanation:
The problem can be broken down into two parts:
Part 1: Rainfall from 7:00 AM to 11:00 AM
The amount of rain during this period is given directly.
\[ \text{Rainfall}_1 = 2.25 \text{ inches} \] Part 2: Rainfall from 11:00 AM to 5:00 PM
First, we need to calculate the duration of this period.
\[ \text{Duration}_2 = 5:00 \text{ PM} - 11:00 \text{ AM} = 6 \text{ hours} \] The rate of rainfall is given as 1.25 inches every two hours. We can find the number of two-hour intervals in these 6 hours.
\[ \text{Number of intervals} = \frac{6 \text{ hours}}{2 \text{ hours/interval}} = 3 \text{ intervals} \] Now, calculate the rainfall during this period.
\[ \text{Rainfall}_2 = 3 \text{ intervals} \times 1.25 \text{ inches/interval} = 3.75 \text{ inches} \] Step 3: Total Rainfall
To find the total rainfall by 5:00 PM, we add the amounts from both parts.
\[ \text{Total Rainfall} = \text{Rainfall}_1 + \text{Rainfall}_2 \] \[ \text{Total Rainfall} = 2.25 + 3.75 = 6.00 \text{ inches} \] Step 4: Final Answer
The total amount of rain that landed on the ground by 5:00 PM is 6 inches.