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If a body covered đť‘‘ 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.
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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.
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So, what this means is it travels 44 metres every minute.
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And weâ€™re told that it was travelling for 10 minutes.
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So, we can say that it covered 44 metres every minute for 10 minutes.
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So, we can calculate đť‘‘, the distance it travelled.
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And thatâ€™s because what we do is we multiply 44, because thatâ€™s the distance every minute, by the number of minutes, which is 10.
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And when we do this, we get 440 metres.
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So, we know that đť‘‘ is equal to 440.
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So have we solved the problem?
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Well, no, because what weâ€™re looking to do is find the time taken to cover this same distance but when the velocity changes.
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And this time, the velocity is 20 metres per minute.
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So this time, if we use the same calculation as before but weâ€™ve got different variables to put into it, weâ€™ve got đť‘‘ because we know itâ€™s 440.
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So, we can say 440 was equal to.
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And then, what we had was our velocity, which this time is 20, multiplied by the number of minutes or the time which Iâ€™ve called đť‘ˇ.
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Well, this is what weâ€™re trying to find out.
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Well, to find out what đť‘ˇ is, what we do is do the inverse operation.
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Instead of multiplying by 20, we divide each side by 20.
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And when we do that, we get 22 is equal to đť‘ˇ.
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And have a quick look at how we worked out 440 divided by 20.
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Well, what we did is weâ€™ve got 440 over 20.
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We can instantly divide through by 10, so we remove the zeroes.
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So then, weâ€™ve got 44 divided by two.
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Well, two goes into four twice, so we get two.
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And two goes into 40 20 times, so we get 22.
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So great, thatâ€™s how we found our value.
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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.
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And what weâ€™ve done is weâ€™ve worked this all out using an adaptation of the speed-distance-time triangle.
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We could show how by having a look at our calculations.
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If we look at the left-hand side, weâ€™ve got distance equals velocity multiplied by time.
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Now, if we interchange velocity with speed, weâ€™ve got distance equals speed multiplied by time which, we can see, would get from our speed-distance-time triangle.
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And then, if we look at the right-hand side, well what we had was 440 which is our distance.
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And then, we divided it by 20 which was, in fact, our velocity or speed if we interchange them.
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And then, this was equal to our time.
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So, we could say that distance over speed equals time, which is what you again would get from our speed-distance-time triangle.