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:

Question

A. 20 seconds
B. 2 minutes
C. 1.5 minutes
D. 5 minutes
E. None of these

How to get a relation between the number of clicks and speed of the train and the time taken by it.

I assumed that the number of clicks has to be an integral value like 1,2,3..... Further i tried to figure out at what distance and at what time the train gives an integral value of the number of clicks. I tried to play with the options.But all in vain.

Answer 1

See how many clicks in 1 minute at 60 mph

60*5280/30*60=176 clicks in 1 minute

But they want to know how many seconds for 60 clicks to occur:

60/176=About 1/3 of a minute, 20 seconds

Answer 2

30 ft (1 m/5280 ft) = .00568 mile

v = .00568 /T in hours

T in hours = .00568 /v

T in seconds = 3600*.00568/v
= 20.45/v

clicks/second = 1/T = v/20.45
so
v = 20.45 * clicks/second

1 click/second --> 20.45 mph
2 clicks/second -->41 mph

v = 20.45 * clicks/second
= clicks/20.45 seconds

so A.

Answer 3

Let the required time be x hr. Speed when distance of one rail is taken is 30 ft / x hr. After converting in miles/ hr we get 0.00568 miles / x hr. So we want to know that at what time 0.00568 / x is the number of clicks heard according to question.

Now we know that we will only hear one click while travelling 30 ft so we want to know at what time 0.00568/ x equals 1 which means x = 0.00568 hence 0.00568 hr is the answer which when converted into seconds give almost 20 seconds.
So A is the answer.