If a body covered 𝑑 metres in 10 minutes with a uniform velocity of 44 metres per minute, find the time taken to cover this distance when the body moves with a velocity of 20 metres per minute.
So, if we take a look at the question, we can see that, first of all, the body was travelling with a uniform velocity of 44 metres per minute. So, what this means is it travels 44 metres every minute. And we’re told that it was travelling for 10 minutes. So, we can say that it covered 44 metres every minute for 10 minutes. So, we can calculate 𝑑, the distance it travelled. And that’s because what we do is we multiply 44, because that’s the distance every minute, by the number of minutes, which is 10. And when we do this, we get 440 metres. So, we know that 𝑑 is equal to 440. So have we solved the problem?
Well, no, because what we’re looking to do is find the time taken to cover this same distance but when the velocity changes. And this time, the velocity is 20 metres per minute. So this time, if we use the same calculation as before but we’ve got different variables to put into it, we’ve got 𝑑 because we know it’s 440. So, we can say 440 was equal to. And then, what we had was our velocity, which this time is 20, multiplied by the number of minutes or the time which I’ve called 𝑡. Well, this is what we’re trying to find out.
Well, to find out what 𝑡 is, what we do is do the inverse operation. Instead of multiplying by 20, we divide each side by 20. And when we do that, we get 22 is equal to 𝑡. And have a quick look at how we worked out 440 divided by 20. Well, what we did is we’ve got 440 over 20. We can instantly divide through by 10, so we remove the zeroes. So then, we’ve got 44 divided by two. Well, two goes into four twice, so we get two. And two goes into 40 20 times, so we get 22. So great, that’s how we found our value.
So therefore, we can say that the time taken to cover 440 metres when the body moves at the velocity of 20 metres per minute is 22 minutes. And what we’ve done is we’ve worked this all out using an adaptation of the speed-distance-time triangle. We could show how by having a look at our calculations. If we look at the left-hand side, we’ve got distance equals velocity multiplied by time. Now, if we interchange velocity with speed, we’ve got distance equals speed multiplied by time which, we can see, would get from our speed-distance-time triangle.
And then, if we look at the right-hand side, well what we had was 440 which is our distance. And then, we divided it by 20 which was, in fact, our velocity or speed if we interchange them. And then, this was equal to our time. So, we could say that distance over speed equals time, which is what you again would get from our speed-distance-time triangle.