Video Transcript
In the diagram shown, the distance 𝐴𝐵 is 120 metres and the distance 𝐵𝐶 is 280 metres. At an average speed of eight metres per second, how much time is taken to move from 𝐴 to 𝐵 and then to 𝐶 by travelling along the two lines shown in the diagram?
Okay, so in this question first of all, we’ve been told that the distance 𝐴 to 𝐵 is 120 metres. And secondly, we’ve been told that 𝐵 to 𝐶 is 280 metres. Now, we also know that we’re going from 𝐴 to 𝐵 along the line shown in the diagram and then from 𝐵 to 𝐶 along the line shown in the diagram. And we’re doing this at an average speed of eight metres per second. We’ve been asked to find the amount of time taken for this entire journey, so going from 𝐴 to 𝐵 and then 𝐵 to 𝐶 at an average speed of eight metres per second.
Well, to work this out, we first need to recall what average speed actually means. We can recall that average speed is defined as the total distance travelled by an object, for example, divided by the time taken for that object to travel that distance. So in our scenario, we’re travelling from 𝐴 to 𝐵 and then from 𝐵 to 𝐶. So the total distance travelled is the 120 metres from 𝐴 to 𝐵 plus the 280 metres from 𝐵 to 𝐶.
So let’s say that the total distance travelled is something that we’ll call 𝑑. And we just said that 𝑑 is equal to 120 metres plus 280 metres. And this ends up being 400 metres. So that’s the total distance travelled from 𝐴 to 𝐵 and then from 𝐵 to 𝐶, 400 metres. As well as this, we know the average speed, which we’ll call 𝑠, during the journey. And we know that it’s eight metres per second. At which point, we know two quantities in this equation. We know the average speed. And we know the total distance traveled. Therefore, we can work out the time taken.
If we abbreviate everything slightly by using the symbols for speed and distance and say that the time taken for this journey, which is what we’re trying to find, is called 𝑡, then we can rearrange our equation by multiplying both sides by 𝑡 divided by 𝑠.
This way, we can see that the 𝑠 up top cancels with the 𝑠 in the denominator on the left-hand side. And on the right-hand side, the 𝑡s cancel. Hence, what we’re left with is 𝑡 is equal to 𝑑 divided by 𝑠. Or, in other words, the total time taken for a journey is equal to the total distance travelled during that journey divided by the average speed. And we know these two quantities. So we can plug them into our equation. We could say that the time taken is equal to 400 metres divided by eight metres per second.
Quickly looking at the units, we can see that the metres in the numerator and denominator cancel. So we’re left with one divided by seconds in the denominator, which is equivalent to seconds in the numerator. Hence, our final answer when we evaluate the right-hand side is going to be in seconds, which is perfectly fine because we’re looking to find the amount of time taken. And that’s going to be in seconds. So 400 divided by eight ends up being 50. And as we said, the unit is going to be seconds.
And therefore, our final answer is that this journey takes a total time of 50 seconds.
