Fill in the blank with the correct numerical value.

Answer:A logistics detachment inspects

30

cargo containers in

45

minutes. Operating at this constant rate, it will take the detachment 【4】 hours to inspect

160

cargo containers.

Since the detachment operates at a constant rate, this is a direct proportion problem. They inspect

30

containers in

45

minutes. Using the proportion

\frac{30}{45} = \frac{160}{x}

, we find it takes

240

minutes to inspect

160

containers. Dividing

240

minutes by

60

minutes per hour gives the final answer of

4

hours.

Set up a direct proportion relating the number of containers to the time in minutes.

\frac{30}{45} = \frac{160}{x}

Because the inspection rate is constant, the ratio of containers to time remains the same.

Solve the proportion for

x

to find the total time required in minutes.

30x = 160 \times 45 \Rightarrow 30x = 7200 \Rightarrow x = 240 \text{ minutes}

Cross-multiplying and isolating

x

determines the unknown time in the same units (minutes) used in the initial ratio.

Convert the total time from minutes to hours.

\frac{240 \text{ minutes}}{60 \text{ minutes/hour}} = 4 \text{ hours}

The question specifically asks for the final answer in hours, requiring a unit conversion.

Direct proportions with unit conversion

Question