Question 1129628: Hello. I am really struggling with my averages right now and I need some help with this question. I'm a 6th grader and not really good at maths, so please try to explain it as simple as you can. So here's my question: The daily average training time of sportsmen A, B and C is 12.2 hours. The daily average training time of sportsmen A,B,C and D is 11.5 hours. What is the daily training time of sportsman D? I suppose that sportsman D's training time is lesser than the other, making the total average of A, B, C and D lower.
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! Your reasoning is correct, D has a lower daily training time because including D brings the average time down.
We can find D's time as follows:
The average of A,B,C is found by adding their times and dividing by 3:
(A+B+C)/3 = 12.2 (eq 1)
The average of A,B,C,D is found by adding their times and dividing by 4:
(A+B+C+D)/4 = 11.5 (eq 2)
In (eq 1), multiply both sides by 3:
3*(A+B+C)/3 = 3*12.2 <—— the left hand side will become 1*(A+B+C) or just A+B+C
A+B+C = 36.6
In (eq 2), multiply both sides by 4:
4*(A+B+C+D)/4 = 4*11.5
A+B+C+D = 46
Now notice we can substitute 36.6 for "A+B+C" in this last equation:
36.6 + D = 46
Finally, subtracting 36.6 from both sides:
36.6 + D - 36.6 = 46 - 36.6
D = 46-36.6
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