1953 AMC 12 Problem 31

Question

The rails on a railroad are

30

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:

20

seconds

2

minutes

1\dfrac12

minutes

5

minutes

none of these

Answer: A

Concepts:unit conversion rate approximation

Difficulty rating: 1540

Small hint:

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

30

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

v

miles per hour is

\frac{22v}{15}

feet per second. Since each click represents

30

feet, the click rate is

\frac{\frac{22v}{15}}{30}=\frac{11v}{225}

clicks per second. In

\frac{225}{11}\approx20.45

seconds, the number of clicks is

v.

The closest listed interval is

20

seconds.

Thus, the correct answer is A.

1953 AMC 12 Problem 31

Answer: A

Difficulty rating: 1540

Small hint:

Big hint:

Solution:

Problem 31 in other years