Video: Pack 4 • Paper 3 • Question 3

Pack 4 • Paper 3 • Question 3

02:09

Video Transcript

John enters a mince pie eating contest. When there are 47 minutes left before the end of the contest, John’s friend Kayla joins the spectators. Kayla overhears the commentator say the following: “John will need to eat 18 more pies to break the all time record.” Kayla says that John will need to eat at a speed of at least 24 pies an hour in order to break the all time record. Is Kayla correct? You must show all of your working.

As there are 47 minutes left, we can say that there are forty-seven sixtieths hours left of the contest. This is because there are 60 minutes in an hour. John needs to eat 18 more pies to break the record. Therefore, we need to divide 18 by forty-seven sixtieths. This will work out how many mince pies he needs to eat per hour.

Dividing by a fraction is the same as multiplying by the reciprocal of this fraction. Therefore, 18 divided by forty-seven sixtieths is the same as 18 multiplied by 60 over 47. This is equal to 1080 divided by 47. In order to break the all time record, John needs to eat at a rate of 22.98 pies per hour. As 1080 divided by 47 is 22.98 to two decimal places.

Kayla said that John would need to eat at a speed of 24 pies per hour. As 22.98 is less than 24, Kayla is wrong. We can say that John does not need to eat at least 24 pies per hour. He is able to beat the record if he eats a 22.98 pies per hour for the remainder of the time.

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