1953 AMC 12 Problem 31

Attempt Problem 31 of the 1953 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1953 AMC 12 solutions, or check the answer key.

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31.

The rails on a railroad are 3030 feet long. As the train passes over the point where the rails are joined, there is an audible click. The speed of the train in miles per hour is approximately the number of clicks heard in:

2020 seconds

22 minutes

1121\dfrac12 minutes

55 minutes

none of these

Answer: A
Concepts:unit conversionrateapproximation
Difficulty rating: 1540
Small Hint:

Convert one mile per hour to feet per second, then divide by 3030 feet per click

Big Hint:

Find the time interval for which the click count is approximately the numerical speed in miles per hour

Solution:

A speed of vv miles per hour is 22v15\frac{22v}{15} feet per second. Since each click represents 3030 feet, the click rate is 22v1530=11v225 \frac{\frac{22v}{15}}{30}=\frac{11v}{225} clicks per second. In 2251120.45\frac{225}{11}\approx20.45 seconds, the number of clicks is v.v. The closest listed interval is 2020 seconds.

Thus, the correct answer is A.

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