Certainly! Let's address each part of the question step by step.
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(i) In what type of proportion are the downloading time and the size of the application file?
The downloading time and the size of the application file are in direct proportion. This means if the size of the file increases, the downloading time will increase proportionally, provided the internet speed remains constant.
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(ii) Find the size of the file in GB applying the proportion method.
Given:
- Download speed = 50 MBps
- Download time = 1 minute = 60 seconds
First, calculate the size of the file in megabytes (MB):
1. File size in MB = speed_initial x download_time_initial_seconds
= 50 MBps x 60 seconds
= 3000 MB.
Now, convert the file size from MB to GB:
1. File size in GB = file_size_MB / 1024
= 3000 MB / 1024
= 2.9296875 GB.
So, the size of the file is 2.9296875 GB.
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(iii) If the internet speed is increased to 75 MBps, how long does it take to download the same size of the application file?
Given:
- New download speed = 75 MBps
We know the file size is 3000 MB. To find the new downloading time:
1. Download time in seconds = file_size_MB / speed_increased
= 3000 MB / 75 MBps
= 40 seconds.
Now, convert the download time from seconds to minutes:
1. Download time in minutes = download_time_increased_seconds / 60
= 40 seconds / 60
= 0.6666666666666666 minutes.
So, it takes approximately 0.6666666666666666 minutes (or 40 seconds) to download the file at 75 MBps.
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(iv) Find the internet speed in MBps required to download the same file in 50 seconds.
Given:
- Desired download time = 50 seconds
We know the file size is 3000 MB. To find the required speed:
1. Required speed = file_size_MB / required_download_time_seconds
= 3000 MB / 50 seconds
= 60 MBps.
So, the internet speed required to download the file in 50 seconds is 60 MBps.
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In summary:
(i) The downloading time and file size are in direct proportion.
(ii) The size of the file is 2.9296875 GB.
(iii) At 75 MBps, the download time is approximately 0.6666666666666666 minutes (or 40 seconds).
(iv) To download the file in 50 seconds, the required internet speed is 60 MBps.
