Answer:
A. 4.33 minutes
B. it will be about 11% less than the initial time (4.85 -0.54)
Explanation:
You want to know the team's final time if it decreases by 5 1/2% on each of two runs after their initial run time of 4.85 minutes. And you want to know how to check the answer for reasonableness.
A. Final run
If the time decreases by 5.5% on each run, it is multiplied by (1 -5.5%) = 0.945 on each run. The time after 2 more runs will be ...
(4.85 min)(0.945)(0.945) ≈ 4.33 min
The team's time on the final run was about 4.33 minutes.
B. Reasonableness check
For small percentages, the product of small percentage changes is nearly the same as the sum of the percentage changes. That is, two changes by -5.5% will be about the same as a change of 2 × (-5.5%) = -11%.
Of course a decrease of 11% is a decrease of 10% and another decrease of 1%. This makes the estimated time be ...
4.85 -0.485 -0.0485 ≈ 4.85 -0.54 = 4.31
The estimate is a larger change than the actual change, so the computed value of 4.33 is judged to be reasonable. (The actual effect of two -5.5% changes is about a -10.7% change.)
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Additional comment
This "add the percentages" is a suitable way to check the reasonableness of all sorts of problems involving percent changes, including problems involving investments or loan interest.
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