Train your brain with PTV - The telegraph poles
On an automobile trip the other day, a driver passed a line of telegraph poles that was 3 5/8 miles* long. With the aid of a stopwatch he discovered that the number of poles that passed per minute, multiplied by 3 5/8 equaled the number of miles per hour that he was travelling.
Assuming that the poles were equally spaced and that he travelled at a constant speed, what was the distance between two adjacent poles.
* a mile = 5,280 feet = 1.6 kilometres
Adapted from: Sam Loyd and Martin Gardner, "Mathematical Puzzles and Games. © 2003 DuMont Buchverlag, Cologne, p. 275
Solution
Let's take x for the total number of poles and y for the number of hours that the driver needed for travelling 3 5/8 miles. The car passes x poles in y hours, i.e. x/y poles in an hour and x/60y poles in a minute.
As we have learned that 3 5/8 times the number of poles per minute equals the driver's speed in miles per hour, we can use the following equation:
3 5/8 x = 3 5/8
______ _____
60 y y
The car's speed of 3 5/8 divided by y is reduced which means the value of x is 60.
As there are 60 poles along the 3 5/8-mile or 19140-feet route, we divide 19140 by 60. So the distance between the poles is 319 feet. The car's speed and the length of the line of poles are no essential data; however there is no clear cut solution for this problem, unless you start and end counting the number of poles that pass per minute when the car is exactly between two poles and the length of the line of poles is calculated in a similar manner.
