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Over the course of 8 races, a runner's finishing time was 5

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by BTGmoderatorDC » Mon Sep 23, 2019 4:34 pm
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
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by Jay@ManhattanReview » Mon Sep 23, 2019 8:34 pm
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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by Scott@TargetTestPrep » Fri Sep 27, 2019 7:33 am
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

Since in each race, the runner was 5 seconds faster (i.e., 5 seconds less) than in the race prior, we can let the time of each race be as follows:

Race 1 = x

Race 2 = x - 5

Race 3 = x - 10

Race 4 = x - 15

Race 5 = x - 20

Race 6 = x - 25

Race 7 = x - 30

Race 8 = x - 35

Thus, the sum of the race times is 8x - 140.

We are given that the total was 44 minutes and 20 seconds. Converting to seconds gives us:

44 minutes and 20 seconds = 44 x 60 + 20 seconds = 2660 seconds

We can now determine x:

8x - 140 = 2660

8x = 2800

x = 350 seconds

350 seconds = 350/60 = 5 and 50/60 minutes = 5 minutes and 50 seconds.

Thus, the time of the second race is 5 minutes 50 seconds - 5 seconds = 5 minutes and 45 seconds.

Answer: D

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