Question Video: Determining Total Distance Traveled

What is the total distance covered by someone who walks along the lines shown in the diagram?

02:35

Video Transcript

What is the total distance covered by someone who walks along the lines shown in the diagram?

Alright, so in this question, we see that we’re presented with a diagram that contains three lines, and we’re asked to find the total distance covered by someone who walks along these lines. Let’s begin by recalling our definition of distance. Distance is defined as the length of the path between two positions. The question tells us that our person walks along the lines, so we see that the path taken by the person in this question must consist of walking along each of these lines in turn. In other words, if they start here, the first part of their path consists of walking along this line, ending up here. We’ll label this line one as it’s the first segment of the path.

The next part of the path that our person follows is this line here. And at the end of it, they end up at this position here. We’ll label this line two. Finally, our person’s path follows this remaining line here, and their final position is here at the end of this line. We’ll label this final line line three. Remember that the question asked us for the total distance covered and that our definition of distance tells us that it is the length of the path that is taken between two positions.

Now we’ve drawn the path that the person from this question takes, and we can see that it consists of three straight line segments which we’ve labeled one, two, and three. If we label the total distance as 𝑑, then we can see that 𝑑, which we know is the length of the path taken, must be equal to the length of line one plus the length of line two plus the length of line three. We are given each of these three lengths in the diagram. So we can substitute these values into our expression for 𝑑. The length of line one is five meters, the length of line two is eight meters, and finally the length of line three is seven meters. And so we have that the total distance covered 𝑑 is given by the sum five meters plus eight meters plus seven meters. If we evaluate this sum, we find that 𝑑 equals 20 meters.

And so we have our answer to the question that the total distance covered by someone who walks along the lines shown in the diagram is equal to 20 meters.

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