About this video
A graph shows Alina's distance A(t) and Bryce's distance B(t) from a science museum over time. The video checks whether A(25) > B(35) by reading each value from the graph (about 32–33 km versus 30 km), so the statement is true. It then tells the story of the trip: who moves fast, who takes breaks, when they catch up, and that Bryce reaches the museum first.
You'll be able to
- read function values like A(25) from a graph.
- compare function values from two graphs and explain what the comparison means.
- describe a journey from a distance-time graph.
Key words
- function notation
- A(t) means the output of function A at time t, here Alina's distance from the museum.
- distance from the museum
- How far away a person still is; it reaches 0 when they arrive.
Transcript
- [Instructor] Two friends are heading to the same science museum. Alina, I guess she's going to be represented by A of t and Bryce represented by B of t, track the time it takes to get home to get from their homes to the museum. The graph shows their distance from the museum in kilometers as a function of time in minutes.
So A of t is essentially the distance that Alina is from the museum, and B of t is the distance that Bryce is from the museum. And let's see what's going on here before I even look at this question here. Alina starts 50 kilometers away. Bryce starts, looks like, I don't know, a little over 45, about 46 kilometers away roughly.
And then they both eventually get there. Let's see what they're asking us. Is the statement A of 25 greater than B of 35 true? Pause this video and have a go at that. Let's see, at time equals 25, that's right over here. A of 25 is right over there. So that is A of 25.
And let's see, B of 35, 35 minutes. B is right over here. This is B of 35, and A of 25 is indeed greater than B of 35. A of 25 looks like it's about, I don't know, 32 or 33 while B of 35 is 30. So this, the simple answer here is yes, but just for the sake of it, let's think about what that means.
That means that Alina at 25 minutes was further away from the museum than Bryce was at 35 minutes. I don't know why you would compare those two times, but that is just true. So what really happens is Alina's going quite quickly to the museum, traveling fast. And at some point Alina catches up, looks like, like right there, catches up with Bryce, and then Bryce starts moving fast and then Alina's, faster than Alina.
And then Alina looks like she's taking a break right over here. And then Bryce takes a break, Alina starts to move, and then she catches up to Bryce again right over here. So Alina catches up to Bryce right at that moment. Then Bryce start, maybe he doesn't want Alina nipping on his heels, and then he starts to move up.
He gets tired maybe, pauses, Alina catches right back up, right over here, passes up Bryce, all the way to here. But then Bryce starts speeding up after taking a break and they catch up right over there. And Bryce takes that really fast pace and keeps going all the way to the end and gets to the museum a good bit earlier than Alina does.
And in that last sprint for both of them, Bryce was going at a faster rate. He started going at that faster rate sooner, and he goes and he just goes at an objectively faster rate. So that's my analysis of this. But the simple answer to the question is yes.
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