A typical 24-hour activity of a mobile crusher plant is shown. The utilization, in %, of the plant, is ______. (round off up to 2 decimals)

Understand the Problem

The question is asking to calculate the utilization percentage of a mobile crusher plant over a 24-hour period based on activity shown in a chart. This involves summing up the working hours and dividing by the total number of hours to get a percentage.

Answer

The utilization percentage of the mobile crusher plant is $20.83\%$.

Steps to Solve

Identify Working Hours

From the chart, we need to identify the hours categorized as "Working hours," which are indicated in white.

Based on the visual provided, the working hours occur from 6 to 7, 8 to 9, and 20 to 23. This means:

Between 6 and 7 there is 1 hour of working time.
Between 8 and 9 there is 1 hour of working time.
Between 20 and 23 there are 3 hours of working time.

Calculate Total Working Hours

Now, we sum the identified working hours: $$ 1 \text{ (from 6 to 7)} + 1 \text{ (from 8 to 9)} + 3 \text{ (from 20 to 23)} = 5 \text{ hours} $$ So, the total working hours is 5.

Find Total Hours in a Day

The total number of hours in a day is 24 hours.

Calculate Utilization Percentage

To find the utilization percentage, we use the formula: $$ \text{Utilization Percentage} = \left( \frac{\text{Working Hours}}{\text{Total Hours}} \right) \times 100 $$ Plugging in the values: $$ \text{Utilization Percentage} = \left( \frac{5}{24} \right) \times 100 $$

Perform the Calculation

Now we calculate the percentage: $$ \frac{5}{24} \approx 0.2083 $$ Thus, $$ 0.2083 \times 100 \approx 20.83% $$

The utilization percentage of the mobile crusher plant is approximately $20.83%$.

More Information

The utilization percentage gives a clear idea of how efficiently the plant is operating over a typical 24-hour period. A higher percentage indicates better utilization and productivity of the equipment.

Tips

Misidentifying the working hours on the chart. It's crucial to carefully observe the color coding and ensure that only "Working hours" are counted.
Forgetting to multiply by 100 in the final step to convert to a percentage.

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