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.
Answers
Anonymous
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
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