Ex: Find the Number of Meters Traveled in 3 seconds Given Kilometers Per Hour

A car is driving at 90
kilometers per hour. How far, in meters, does
it travel in three seconds? So to answer this question
we’ll first convert 90 kilometers per hour
into meters per second, then determine the distance
traveled in three seconds. To do this conversion
we’ll use unit fractions, so begin by writing 90 kilometers
per hour as a fraction, which would be 90 kilometers per one hour. And our goal here is to
convert this rate into a rate where we have meters per second. Let’s begin by converting
the kilometers to meters. We’ll do this using the conversion that one kilometer equals 1,000 meters. So we’re going to multiply
it by a unit fraction, and because we want
kilometers to simplify out, we’ll put kilometers in the denominator, and meters in the numerator. And again, the conversion
is that 1,000 meters equals one kilometer. Because these units are equal, this fraction is equal to one, but notice how the units of
kilometers now simplifies out, leaving us with meters. Now we still have to
convert hours to seconds, so we’ll first convert hours to minutes by multiplying by another unit fraction. We don’t want hours in our
answer, so we’ll have to have hours in the numerator and
minutes in the denominator. And the conversion is that
one hour equals 60 minutes, so we’ll have one hour over 60 minutes. Notice now the units of
hours simplifies out, and now we’re left to
convert minutes to seconds. So we multiply it by
another unit fraction. We want minutes to
simplify out, so we’ll have minutes in the numerator and
seconds in the denominator, and our conversion is that
one minute equals 60 seconds. Minutes simplifies out. Notice how now we have the correct units, so now I’ll multiply across the numerator, multiply across the denominator, and then divide to get the unit rate. So in the numerator we have 90 times 1,000 times one times one, that’s 90,000 meters. And in our denominator
we have one times one times 60 times 60
seconds, or 3,600 seconds. Again, we’ll now convert
this to a unit rate by performing this division. So 90,000 divided by 3,600 is equal to 25 which means that unit rate is 25 meters per one second, which can also be written
as 25 meters per second. But our goal here is to
find the distance traveled in three seconds, where
distance equals rate times time. So the distance traveled is
equal to 25 meters per second times the time of 3 seconds,
which gives us 75 meters. A lot of times when working
with a distance formula we leave the units off like we did here, and then just put the units in our answer. But I do want to show this
again leaving the units in. We could have written this
as the distance equals the rate of 25 meters per one second times a time of three seconds,
which can be written as three seconds over one. Notice how in this form the
units of seconds simplifies out leaving us with the same
result of 75 meters. So one thing nice about
leaving the units in is that we never have to
second-guess ourselves about what the unit should
be because the units work themselves out. I hope you found this explanation helpful.

One thought on “Ex: Find the Number of Meters Traveled in 3 seconds Given Kilometers Per Hour

Leave a Reply

Your email address will not be published. Required fields are marked *