Real-Life Math -- Solution
The easiest way to solve this math problem is to convert everything
to bits. We know that the modem line will transmit data at 56 kilobits per
second. We know that a kilobit is equal to 1,024 bits.
So
56 kilobits per second x 1,024 bits per kilobit = 57,344 bits per second
The
modem line transmits 57,344 bits per second.
The file we want to download
is 12 megabytes.
12 megabytes x 1,048,576 bytes per megabyte
x 8 bits per byte = 100,663,296 bits to download
100,663,296
bits / 57,344 bits per second = 1,755 seconds (29.25 minutes)
It
will take 29.25 minutes for the modem line to transmit a 12-megabyte file.
The
Ethernet connection transmits data at a rate of 10 megabits per second. We
want to translate megabits into bits.
10 megabits
per second x 1,048,576 bits per megabit = 10,048,576 bits per second
We
already know that the 12-megabyte file is equal to 100,663,296 bits.
100,663,296
bits to download / 10,048,576 bits per second = 10 seconds
It
only takes 10 seconds to download the 12-megabyte file by the Ethernet connection.
1,755
seconds - 10 seconds = 1,655 seconds (27.5 minutes)
The
Ethernet connection is 27.5 minutes faster than the modem line.
An
undergraduate math degree and postgraduate degree in computing science help
Grace Patterson get her work done. Patterson is the clinical informatics coordinator
of the faculty of medicine at Dalhousie University.
She says her understanding
of math helps in areas like decision-making, educational techniques, understanding
statistics and more.
"Mathematical programming is one of the models
for decision analysis," she says. "It takes the approach that reality can
be simplified and represented as a set of mathematical relationships."