BTGmoderatorDC wrote:Over the course of 8 races, a runner's finishing time was 5 seconds faster each race than the race prior. If her combined total for all 8 races was 44:20, what was her finishing time for the second race?
A. 5:30
B. 5:35
C. 5:40
D. 5:45
E. 5:50
OA D
Source: Veritas Prep
Say the time taken in the first race = x seconds; thus, the time taken in the second race = (x - 5) seconds; the time taken in the third race = (x - 2*5) = (x - 10) seconds; the time taken in the fourth race = (x - 3*5) = (x - 15) seconds; ... ; the time taken in the eighth race = (x - 7*5) = (x - 35) seconds
So, the sequence of 8 times is x, (x - 5), (x - 10), (x - 15), ... , (x - 35).
Since the above sequence of 8 times has equally spaced numbers, the sum of 8 times = 8*(Average of the first term and the last term) = 8*[x + (x - 35)]/2 = 8x - 140
We are given that the combined total for all 8 races was 44:20 = 44*60 + 20 = 2660
8x - 140 = 2660 => x = 350 sec = 5 minutes and 50 seconds
Thus, her finishing time for the second race = x - 5 = 5 minutes and 50 seconds - 5 seconds = 5 minutes and 45 seconds
The correct answer:
D
Hope this helps!
-Jay
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