Video Transcript
William counted his strides while
walking. He found that he walked at a
constant speed as the number of strides were proportional to the walking time. The table shows how many strides he
had taken at different times. What is the constant of
proportionality between the walking time and the number of strides, i.e., his
speed?
When we think about this constant
of proportionality, specifically, the speed with which William walked, we should be
considering the unit rate for which he was walking. And that means we’ll have a
decision to make. Are we looking for the number of
seconds per stride? Or are we looking for the number of
strides per second? One simple way to think about speed
is the measured distance traveled per unit of time. And so we can choose strides per
second as the unit rate. We know that it takes four seconds
to walk six strides for William. We can write that ratio six strides
out of four seconds.
Since the unit rate needs to be one
second, we divide four by one to get one. And if we divide by four in the
denominator, we need to divide by four in the numerator. Six divided by four is one and a
half. And so we can say that William
walked one and a half strides in one second.
It might be worth checking a few of
the other data points to make sure that this is the constant rate he was
walking. From the table, we know that, in 30
seconds, William walked 45 strides. If we take the unit rate and
multiply it by 30 seconds, we should get 45 strides. When we multiply the numerators,
1.5 times 30 does equal 45. We could also multiply 1.5 by 60
which would give us 90, 90 strides in 60 seconds. And 1.5 times 10 seconds also
equals 15 strides. We found his speed, his rate, to be
1.5 strides for every one second. And we can write that constant of
proportionality as the number 1.5 with the units strides per second.
