Question

In a race, a long distance runner took 3 minutes and 45 seconds to run the first kilometer, and in each succeeding kilometer, 12 seconds more than the preceding kilometer. Find the total running distance after 40 minutes.

Answer 1

first one = a = 3*60 = 180 seconds
change each kilometer = d = 12 seconds
so time for each kilometer = 180 + 12 ( n-1)
arithmetic sequence
sum of times for n kilometers = (n/2) [ 2a + (n-1)d ]
( google arithmetic sequence math is fun)
so
40*60 seconds = (n/2) [ 360 + (n-1)(12) ]
2400 = 180 n + 6 n^2 - 6 n
6 n^2 + 174 n -2400 = 0
n^2 + 29 n - 400 = 0
n = 10.2 or -38.2 use 10.2 kilometers