### Fitness App Challenge -- An Example of Creating Variations to Understand Simple Things Deeply

My fitness app gives me monthly challenge related to exercise each month. In June, the challenge was to complete 3600 minutes of exercise in the month. This averages to 120 minutes/ day as there are 30 days in the month of June. That means, If I do 120 minutes exercise each day of the June month, I total 3600 minutes which is equal to the challenge minutes.

Average does this only. If average monthly expense in first 8 months of this year in your family is ₹25000, that means the total expense is ₹25000*8 = ₹200000. It is not necessary that the monthly expense is ₹25000 each month to keep the average same. Expenses may be high in some months and may be low too in some months. If the total expense in 8 months is ₹200000, then the average monthly expense is same ₹25000.

Coming back to the exercise challenge. Doing 120 minutes of exercise each day was good enough for the June challenge. But, it's quite uncomfortable to keep doing that each day for 30 days. So, I divided the target of 3600 minutes into 2 equal parts and planned to do the first part at 150 minutes per day and second part at 90 minutes per day. Average of 150 and 90 is 120 which is same as the average required for the target.

Some of you might be thinking that it's not going to work. You are right. You do all the calculation and check. It takes 32 days to complete 3600 minutes of exercise. June month has only 30 days. So, what went wrong?

If I exercise for 120 minutes every day, I reach the target of 3600 minutes in 30 days. But, if a divide the target in two equal parts and do them at 150 minutes/ day and 90 minutes/days respectively, it takes 32 days even though the average of 150 and 90 is 120. Try with different pair of numbers with average 120 only and see how many days it takes to complete the challenge. Can you identify how the number of days required to meet the challenge varies depending on the plan? Can you suggest two different numbers whose average is 120 but helps in completing the target in less than 32 days time? Can you have such pair for 30 days or lesser than that?

You will be able to answer all these without doing any calculation after understanding the finer points of the concept. This doesn't require complex mathematical concepts. Anyone can try and enjoy a right way of learning mathematics. You may find examples of things going wrong in similar way in your area of work as well.

Numbers have been selected in this example to keep the computation simple and allow you to experiment with the situation. So try, understand and build a right habit of understanding simple things deeply.