Each crop duster who works for Gary's Crop Dustin' 4 Cheap can dust half an acre of crops in 25 minutes. The company must dust eight 0.75-acre lots and twelve 1.5-acre lots to complete a certain jod. What is the minimum number of crop dusters needed to complete the jod in 5 hours?

Options

A. `4`
B. `5`
C. `6`
D. `7`

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the time taken by one crop duster to dust one acre.
Given that one crop duster can dust half an acre in 25 minutes, we can find the time taken to dust one acre.

\[ \text{Time for 0.5 acres} = 25 \text{ minutes} \]
\[ \text{Time for 1 acre} = 25 \text{ minutes} \times 2 = 50 \text{ minutes} \]

### Step 2: Convert the time from minutes to hours.
To convert 50 minutes into hours, we divide by 60 (since 1 hour = 60 minutes).

\[ \text{Time for 1 acre in hours} = \frac{50}{60} = \frac{5}{6} \text{ hours} \]

### Step 3: Calculate the total area that needs to be dusted.
We need to dust eight 0.75-acre lots and twelve 1.5-acre lots. We calculate the total area:

\[ \text{Total area} = (8 \times 0.75) + (12 \times 1.5) \]
Calculating each part:
\[ 8 \times 0.75 = 6 \text{ acres} \]
\[ 12 \times 1.5 = 18 \text{ acres} \]
Adding these together:
\[ \text{Total area} = 6 + 18 = 24 \text{ acres} \]

### Step 4: Calculate the total time required for one crop duster to dust the total area.
Now we find out how long it takes for one crop duster to dust 24 acres.

\[ \text{Total time} = 24 \text{ acres} \times \frac{5}{6} \text{ hours per acre} \]
Calculating this:
\[ \text{Total time} = 24 \times \frac{5}{6} = \frac{120}{6} = 20 \text{ hours} \]

### Step 5: Determine the number of crop dusters needed to complete the job in 5 hours.
If one crop duster takes 20 hours, we need to find out how many crop dusters are required to complete the job in 5 hours.

Let \( x \) be the number of crop dusters needed. The equation is:
\[ \frac{20 \text{ hours}}{x} = 5 \text{ hours} \]
Solving for \( x \):
\[ x = \frac{20}{5} = 4 \]

### Conclusion
The minimum number of crop dusters needed to complete the job in 5 hours is **4**.

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