Elementary My Dear
David Taylor drove at a steady speed along the highway, his wife beside him. "Have you noticed," he said, "that those road signboards seem to be regularly spaced along the road? I wonder how far apart they are."
Mrs. Taylor glanced at her wristwatch, then counted the number of signboards they passed in one minute. "What an odd coincidence!" exclaimed Taylor. "When you multiply that number by 10, it exactly equals the speed of our car in miles per hour."
Assuming the car's speed is constant, that the signs are equally spaced, and Mrs. Taylor's minutes began and ended with the car midway between two signs, how far is it between one sign and the other?
Mrs. Taylor glanced at her wristwatch, then counted the number of signboards they passed in one minute. "What an odd coincidence!" exclaimed Taylor. "When you multiply that number by 10, it exactly equals the speed of our car in miles per hour."
Assuming the car's speed is constant, that the signs are equally spaced, and Mrs. Taylor's minutes began and ended with the car midway between two signs, how far is it between one sign and the other?
Labels: friday special, mathemagic, puzzle
posted by Rajesh Lal at
8:04 PM
12 Comments:
They are going 60mph
10 signs in one minute = 600 in one hour
600 / 10 = 60 mph
so....
in one minute they travel 1 mile
so ...
there is a tenth of a mile between each sign
Right?
He passed 6 signs in a minute; 6 times 10 equals 60; he was going 60 miles per hour; so a mile per minute; I can only assume that the distance between one sign and the other sign is 1/5 of a mile.
Okay...
if 30mph = 3 signs in a minute
--> 1 minute = 1/2 mile
--> 1/2 / 3 = 1/6 of a mile
if 40mph = 4 signs in a minute
--> 1 minute = 2/3 mile
--> 2/3 / 4 = 1/6 of a mile
if 50mph = 5 signs in a minute
--> 1 minute = 5/6 mile
--> 5/6 / 5 = 1/6 of a mile
if 60mph = 6 signs in a minute
--> 1 minute = 1 mile
--> 1 / 6 = 1/6 of a mile
Therefore, whatever speed they were going at, the space between the lamposts is always going to be 1/6 of a mile
This can probably be put into algebra to prove it -
L = number of lamposts
M = speed of car in mph
d = distance between lamposts
so... d = (M/60) / L
(-where M/60 calculates the miles per minute the car travels-)
d = (M/60) / L
d = M/60 x 1/L
d = (Mx1)/(60xL)
d = M/60L
since the mph will always be ten times the number of lamposts, i can substitute in M=10 and L=1
d = 10/60
d = 1/6
Hope that makes sense
-Emily
Wow Emily,
I was thinking something along the lines and was working with different numbers.
But I couldn't make the Algebra equation :( kudos to you.
Emily's right but rather long-winded. Here's a simpler proof:
n = no of signs passed per minute
d = distance apart im miles
Then n x d x 60 = distance per hour
= speed = 10 x n
Cancelling out 10 x n from each side gives us d x 6 = 1
i.e. d = 1/6 miles = 880 feet
you are making one assumption that is not in the language of the question: that the speed is being measured in miles per hour.
yes, she says it, but does the tool of meaurement actually measure in that way? The structure of the question gives us absolutes for the rest...or does it. She is looking at her watch. She is looking at the speed. She is assuming the tools are accurate (and the author is giving you her level of certainty). All of these imaginings rely on this flaw...or these flaws. But that is the fun of the lie of certainties and proofs.
You guys make my brian hurt >.<
Emily again...
I know that was a bit long winded, but that's just the way my brain works, sorry, i was trying not to make it too confusing aswell
Tim... if you notice the last paragraph starts with 'assuming...'
you're right, and none of these things would be entirely accurate,
but if you started saying if this was one second out...etc, how many different answer would you get
this question is just about the maths with the info given in the question
Emily your reasoning is flawless! keep it up and congrats for the maths!
-gilumar-
How fast were they going????
6 meters?
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