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Question

Difficulty: MediumDirect Proportions

Complete the statement below by calculating the missing numerical value. Enter only the number.

Answer:A military satellite uplink transmits 1.51.5 gigabytes of reconnaissance data every 4040 seconds. Operating at this constant rate, it will take 【8】 minutes to transmit a total of 1818 gigabytes of data.

Answer

8
By setting up a proportion, we find that transmitting 1818 gigabytes takes 480480 seconds. Dividing 480480 seconds by 6060 gives exactly 88 minutes.

Step-by-Step Solution

1
Set up a direct proportion comparing data volume to time.
1.540=18x\frac{1.5}{40} = \frac{18}{x}
Because the transmission rate is constant, the ratio of gigabytes to seconds remains the same.
2
Solve for the unknown time xx in seconds by cross-multiplying.
1.5x=40×18→1.5x=720→x=4801.5x = 40 \times 18 \rightarrow 1.5x = 720 \rightarrow x = 480 seconds
Cross-multiplication isolates the variable, giving the total time required in seconds.
3
Convert the total seconds into minutes.
480÷60=8480 \div 60 = 8 minutes
The question specifically asks for the time in minutes, so the time in seconds must be divided by the number of seconds in a minute (6060).

Key Concept

Direct proportions with unit conversions
Estimated Time:1m 30s
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Topics

Direct Proportions

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