Video Transcript
To help track how much exercise they do, a person wears a device that counts the number of steps they take. At the end of the day, the device recorded that 5,673 steps had been taken. The person measures their stride length as 0.48 meters. What distance did the person walk? State your answer to the nearest meter.
Okay, so this is a question about distance traveled. We have a person wearing a device that counts the number of steps that they take. We’re told that at the end of a particular day, the devices recorded that they’ve taken 5,673 steps. We are also given the stride length of this person as 0.48 meters. And we are asked to work out what distance the person walked during the day. Let’s begin by recalling the definition of distance.
Distance is defined as the length of a path between two positions. So in our case, those two positions are the position at which the person starts their day and the position at which they end it. And since the distance is just the total length of the path between those two points, it doesn’t matter in what direction the person was walking throughout the day. Their journey could have been a straight line, in which case they’d end up some way from home at the end of the day. Perhaps more likely is that their journey is some completely arbitrary path beginning and ending at the same location, their bed.
In any case, the distance traveled is the total length of this path. In other words, every step that they take contributes to the distance traveled. With that in mind, we can essentially think of this question as a matter of conversion of units. The fitness tracker device measures the distance traveled in terms of number of steps taken. So the person in this question has traveled what we could call a distance of 5,673 steps. Now we want to convert this to an actual distance measured in meters. We are told that this person’s stride length is 0.48 meters. This means that the distance they travel by taking one step is equal to 0.48 meters. And we can assume that this is true for every step that they take.
If with each step they travel 0.48 meters, we could express this as the statement that their distance per step is equal to 0.48 meters per step. Then to get the total distance traveled in the day in terms of meters, we need to take this so-called distance in terms of number of steps and multiply it by the distance covered per step. Remember that we said that we could basically think of this as a conversion of units. So if we look at the units here, we should see that what we’re doing makes sense. If we look at the right-hand side of our equation, we see that the first term, a so-called distance measured in steps, has units of steps. And then we multiply this by a second term, the distance per step, and this term has units of meters per step.
So then, looking at the units, we see that the steps cancel out, and we’re left with a distance measured in meters. And this is exactly the left-hand side of our equation and what we’re trying to find. Now it’s time to put some numbers into this equation. Our first term on the right-hand side, the distance measured in steps, is equal to 5,673 steps. So let’s put this in. Our second term, the distance per step, is given by 0.48 meters per step. So let’s put this one in as well.
Then we have that the distance walked by the person in meters is given by 5,673 steps multiplied by 0.48 meters per step. If we do this multiplication, we get that this distance is equal to 2,723.04 meters. But looking back at the question, we see that were asked to state our answer to the nearest meter. So our result rounds down. And we have our answer to the question that, to the nearest meter, the distance walked by the person during the day is 2,723 meters.
