A teacher takes three hours to mark 75 examination papers. Working at this rate, how many examination papers would they mark in three-fifths of an hour?
We are told in the question that the teacher took three hours to mark 75 examination papers. Our usual method for a question like this would be to work out the unit rate. How many papers would be marked in one hour? We could do this by dividing both sides of the equation by three. Three divided by three is equal to one. 75 divided by three is equal to 25. Therefore, the teacher would mark 25 papers per hour or in one hour. This unit rate would enable us to calculate the number of papers marked in two hours, four hours, seven hours, or any number of hours. We could do this by multiplying 25 by the number of hours.
In this question, we want the number of papers marked in three-fifths of an hour. So we need to multiply 25 by three-fifths. In order to carry out this multiplication, we could cross cancel. Five and 25 are both divisible by five. As this leaves us with five multiplied by three, then 25 multiplied by three-fifths is 15.
An alternative method would be to split 25 into fifths. One-fifth of 25 is equal to five. This shows us once again that three-fifths of 25 is 15. In relation to our question, the teacher would mark 15 papers in three-fifths of an hour.
There is a slightly quicker method we could’ve used in this question. To get from three hours to three-fifths of an hour, we divide by five. This means that we could’ve divided 75 by five to get our answer of 15 papers.