A woman jogging at an average speed of four metres per second runs from position A to position B in a time of 280 seconds. What is the distance between A and B?
Alright, so in this question, we’ve got a woman jogging from let’s say A, which is here, to B, which is here. And she does this in a time, which we’ll call 𝑡, of 280 seconds. As well as this, we’ve been told that her average speed, which we’ll call 𝑠, is four metres per second.
And with this knowledge, we need to find the distance between A and B. Let’s call this distance 𝑑. So at this point, we need to recall a relationship between the distance travelled 𝑑, the average speed 𝑠, and the time taken to travel that distance, 𝑡.
Well, the relationship we’re looking for is the following. The average speed of an object, or in this case a runner, is defined as the total distance travelled by that object, or in this case runner, divided by the time taken to travel that distance. And so we have a relationship between 𝑠, 𝑑, and 𝑡. This means we can rearrange to find the value of 𝑑.
We can do this by multiplying both sides of the equation by the time taken 𝑡. This way, it cancels on the right-hand side. And the only thing we’re left with on the right is 𝑑. In other words, the amount of time taken by the jogger to get from A to B multiplied by her average speed is equal to the distance between A and B.
So now that we know this, we can plug in our values. We can say that the distance travelled by the jogger, which is equal to the distance between A and B, is equal to the time taken, that’s 280 seconds, multiplied by the average speed, which is four metres per second.
Now, looking at the units, we can see we’ve got seconds in the numerator and denominator. And those cancel, leaving us with just metres in the numerator. This is perfectly fine because we’re trying to find the value of a distance. And a distance can be measured in metres. So all we need to do now is to evaluate 280 times four. This ends up being 1120. And as we already said, the unit is going to be metres.
Therefore, we have our final answer. The distance between A and B is 1120 metres.