KBGS Old Boys' Forum

A place to discuss Keighley Boys' Grammar School. 

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KBGS Old Boys' Forum
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The ladder problem.

There is an alleyway between 2 brick walls. Looking down the alley (or maybe it should be snicket) , one ladder rests on left side wall with its base at the bottom corner of the right hand wall, and another rests on the right hand wall with its base at the bottom of the left hand wall.
They are 12 ft and 18 ft long respectively, and cross 6ft from the ground.
How wide is the alleyway ?
Trevor had the practical approach for solving this, but it appears his drawing skills could be improved.
"draw it to scale and measure it - 8.4ft."
The actual distance is 7.387114ft.
I used CAD software to draw the diagram and measure the distance. You can see a video of how I did this on my web site at:

The math involved in calculation would seem to require calculus, since the distance between the walls varies as the height of the crossover point. Because the top ends of the ladders are constrained to move vertically and the pivot points are constrained to be vertically under the top ends, and the lengths are fixed only two variables remain.
The distance between the walls is zero for a crossover height of 12ft., and a maximum of 12ft. for a crossover height of 0ft.
As of now I am not up to setting up an appropriate equation. perhaps someone else can?

Years at KBGS e.g. 1958-1964 (optional) 52-57

Current location (optional) USA

Re: The ladder problem.

Good one Bernard,
yes, it was a rough drawing I did in Illustrator but I didn't think I'd be that far out. My experience with Calculus is too far distant now - as you say, someone else can do it.


Re: The ladder problem.

Maybe I read the scale incorrectly - I got the .4 bit right!

And anyway, who'd make a snicket 7.4ft wide???

Re: The ladder problem.

My main concern is the health and safety issue raised by blocking off a ginnel in such a manner. No mention was made of either signage or safety cones.

Re: The ladder problem.

The H and S issues are important. Leaving ladders across ginnels is dangerous. As 1st formers after Music in the bowels of the Mechanics last period before Friday dinner, we took it as a challenge to ignore Paul Greenwood's directions and would make a dash to run through a dark corridor which opened onto the basement level of Cavendish Street and thence the world was our oyster. One such Friday someone had lent (?) (Yes!) a ladder across the corridor - and being the leading escapee I ran smack into it - at nose height. Despite my practical experience, I cannot offer a solution to the theoretical problem. (I think Bernard Johnson was one stride behind me at the crucial moment.)

Years at KBGS e.g. 1958-1964 (optional) 52-60

Current location (optional) Lincoln

Re: The ladder problem.

The first time I went up a ladder was down a well!!!!!!!!!!!!!!
True story,one day on our way down to football at Lawkholme,a window cleaner was at work at a building in Alice Street. We were joking about it being bad luck to walk under a ladder,and my mate,the late Derek Stow, was laughing and and walked under with his bag on his head while looking up to avoid falling objects,AND put his foot in the bucket of water. Cheers.

Years at KBGS e.g. 1958-1964 (optional) 47-51

Current location (optional) Auckland,NZ