Answer to Question #242407 in Algebra for Mizan

Question

A long-distance runner runs the first kilometre of a race in 3 minutes 45 seconds but finds that his speed drops steadily such that each kilometre takes him 12 seconds more than the preceding one. Find his time (in minutes and seconds) for the 11th kilometre.

Answer 1

If A1 = 225 seconds, and d = 12, then using the formula for arithmetic progression:

$A11 = A1 + (n - 1)×d = 225 + (11 - 1)×12 = 345$

seconds or 5 minutes 45 seconds.