Final answer:
The expression n+0.08n is true for calculating the time it takes Landry to swim a mile if it takes him 8% longer than anticipated. The expression accounts for the additional time by adding 8% of the anticipated time 'n' to itself, correctly giving the total swim time.
Step-by-step explanation:
The student's question is asking whether the expression n+0.08n correctly calculates the time it takes for Landry to swim a mile, given it takes him 8% longer than anticipated. The answer to this question is true. Let's break down why this is the case.
If it takes Landry 'n' minutes to swim a mile, we calculate 8% of 'n' by multiplying 'n' by 0.08, which gives us 0.08n. To find the total time it takes, including the added 8%, we then add 0.08n to 'n'. Therefore, the expression n+0.08n represents Landry's anticipated time plus the additional 8%, giving us the total time it takes him to swim a mile.
Using algebra, we can further simplify the expression n+0.08n by combining like terms, which results in 1.08n. This simplified expression shows that Landry's actual time to swim a mile is 108% of his anticipated time, which indeed is 8% longer.