Video Transcript
A jet airplane travels at 0.55
kilometers per second. Air traffic control needs this
speed in miles per hour. Converting from kilometers per
second to miles per hour is a two-stage process. What is this speed in kilometers
per hour? What is this new speed in miles per
hour?
Okay, so this question gives us the
speed of a jet airplane in units of kilometers per second. This speed is needed in units of
miles per hour. We’re told that it’s going to be a
two-stage process to convert from kilometers per second to miles per hour. We’ve got two parts to this
question, and each of them is one of these two stages.
The first part is asking us to
convert the speed from kilometers per second into kilometers per hour. To do this, we can recall that
there are 60 seconds in one minute and there are 60 minutes in one hour. In other words, one second is equal
to one sixtieth of a minute and one minute is equal to one sixtieth of an hour. We are told that the jet airplane
travels at a speed of 0.55 kilometers per second. This means that it travels a
distance of 0.55 kilometers in each one-second interval of time.
Now, we know that one second is
equal to one sixtieth of a minute. This means that 0.55 kilometers
divided by one second must be equal to 0.55 kilometers divided by one sixtieth of a
minute. We can also write one sixtieth of a
minute as one over 60 multiplied by one minute. But we also know that one minute is
equal to one sixtieth of an hour. So, on the right-hand side of this
expression, we can replace the one minute with one sixtieth of an hour. So we have that our speed of 0.55
kilometers per second is equal to 0.55 kilometers divided by one over 60 times one
over 60 hours. Evaluating this bit in the
denominator on the right-hand side, we have that 0.55 kilometers per second is equal
to 0.55 kilometers divided by one over 3600 hours. We could equally write this as 0.55
divided by one over 3600 kilometers per hour.
Whenever we have a fraction within
a fraction of the form 𝐴 divided by one over 𝐵, then that’s exactly the same as 𝐴
multiplied by 𝐵. In this case, that means that the
0.55 divided by one over 3600 on the right-hand side of this expression is simply
equal to 0.55 multiplied by 3600. So we’ve got that 0.55 kilometers
per second is equal to 0.55 multiplied by 3600 kilometers per hour.
This expression actually gives us
another way of looking at this problem. A speed of 0.55 kilometers per
second means that the jet airplane travels a distance of 0.55 kilometers in each
one-second interval of time. In the same way, a speed in
kilometers per hour will give us the number of kilometers that the jet airplane
travels in each one hour of time. Since there’s 60 seconds in each
minute and 60 minutes in each hour, then there must be 60 multiplied by 60 seconds
in each hour, and this works out as 3600. Since one hour lasts for 3600 times
as long as one second, then in one hour we would expect the jet airplane to travel
3600 times as far as it would in one second. So the value of the speed in units
of kilometers per hour, which is the number of kilometers traveled per one hour of
time, is 3600 times the value of speed in units of kilometers per second.
When we evaluate this expression
for the speed in kilometers per hour, we get a result of 1980 kilometers per
hour. And so our answer to this first
part of the question is that the speed of 0.55 kilometers per second in units of
kilometers per hour is equal to 1980 kilometers per hour.
Okay, let’s clear some space so
that we can look at the second part of the question.
What is this new speed in miles per
hour?
Okay, so the first part of the
question was converting from kilometers per second to kilometers per hour. And now in this second part of the
question, we’re asked to take this speed in units of kilometers per hour and convert
it into miles per hour. We can recall that one mile is
approximately equal to 1.6 kilometers. Actually, we’re going to be a
little bit more precise here and use the conversion that one mile is approximately
1.60934 kilometers. We’ll treat this conversion rate as
being exact.
Now, if one mile is equal to
1.60934 kilometers, then one kilometer must be equal to one over 1.60934 miles. We know that the speed is 1980
kilometers per hour. And we also know that each one of
these 1980 kilometers is equal to one divided by 1.60934 miles. So we can convert our distance of
1980 kilometers into units of miles by multiplying by this conversion factor. And since the jet airplane travels
1980 kilometers per hour of time, then this expression here must be the number of
miles traveled per hour.
Evaluating the expression gives us
a speed of 1230.318 miles per hour, where the ellipses indicate that there are
further decimal places. Let’s round this to the nearest
whole number of miles per hour and notice that miles per hour is commonly
abbreviated as mph. So our answer to the second part of
the question is that the speed of the jet airplane in units of miles per hour is
equal to 1230 miles per hour.
