Video: AQA GCSE Mathematics Higher Tier Pack 4 • Paper 2 • Question 7

A group of 7 motorbikers competed in a quarter-mile drag race. The times of 6 of the motorbikers in seconds are shown in the grid. The mean time for all 7 motorbikers was 9.98 seconds. Calculate the racing time of the 7th motorbiker. You must show your working.

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Video Transcript

A group of seven motorbikers competed in a quarter-mile drag race. The times of six of the motorbikers in seconds are shown in the grid. The mean time for all seven motorbikers was 9.98 seconds. Calculate the racing time of the seventh motorbiker. You must show your working.

The mean time equals the sum of all motorbiker times divided by the number of motorbikers. We’re missing the race time of the seventh motorbiker. We can let 𝑡 equal the seventh motorbiker’s time.

We’re told that the mean time is 9.98 seconds, which equals the sum of all the times divided by the number of motorbikers, which is seven. If we’re trying to solve for our missing value of 𝑡, we need to get 𝑡 by itself. We can do that by multiplying both sides of the equation by seven. 9.98 times seven equals 69.86. And on the right side, the sevens have cancelled out, leaving us with only what’s in the numerator.

We can also go ahead and add the other six racing times together. When we do that, we get 59.98. And then we bring down our plus 𝑡. Remember, we’re trying to solve for 𝑡, to get 𝑡 by itself. We do that by subtracting 59.98 from both sides of the equation. 69.86 minus 59.98 equals 9.88. The 𝑡-value equals 9.88. 𝑡 equals 9.88 seconds, which means the seventh motorbiker finished the race in 9.88 seconds.

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