What is the total distance walked by someone along the lines shown in the diagram?
Okay, so in this question, we can see that we’ve got three different lines, one of which is 15 meters long. The other is 10 meters long. And the final one is 20 meters long. We’ve been asked to find the total distance walked by someone along these lines.
Well, we can recall that distance is defined as the length of the path between two positions. So if someone were to walk from here and only walk along the first line until they got to this position here, then the distance that they would’ve walked would be the length of the path that they’d taken between these two positions. And like we said, they walked along the line. So they would’ve travelled 15 meters. And we could apply this same logic to the other two lines.
However, we’ve been asked to find the total distance walked by someone along these lines. So we need to find out the entire distance walked by someone starting here and then going to this point along the line, and going from there along the line to this point, and then finally walking along this line to the final point. We need to work out that total distance.
Well, that total distance is the total length of the path walked by the person along these lines. In other words, it’s equal to 15 meters plus 10 meters plus 20 meters. And so, we can say that the distance travelled by the person, which we’ll call 𝑑, is equal to 15 meters, that’s the length of the first line, plus 10 meters, that’s the length of the second line, plus 20 meters, that’s the length of the third line.
And when we evaluate this, we find that this total distance is equal to 45 meters. Hence, we found our final answer.