Name: Jennifer
Level: Secondary
Question:
Scott is a homebuilder. He builds railings in which he places spindles.
Spindles ar evertical posts taht are equally spaced beneath a horizontal
bar. Scott would like a mathematical model to help him determine the amount
of space to put between each spindle. The railing must follow the following
criteria: The spaces between each spindle must be equal except for the
ones at either end. Theses spaces are smaller. They are half the width
of a spindle less than the other spaces. The number of spindles needs
to be minimized since spindles are costly.
Help Scott determine what width of space to use between the spindles. Create a mathematical model to determine the width of space between each spindle in termso f the number of spindles. Use an 8' (96") railing that has 2 1/2" wide spindles. Explain your thinking. For safety reasons the maximum width of a space is 4"
Generalize you model to determine the width of spaces for total railing of length L and spindle width s
Hi Jennifer,
The problem would be easier if all the spindles were the same distance apart. The end two spindles create a complication. What I suggest is to imagine extending the railing by 2 1/2", equally space the spindles and then move the end two spindles in 1 1/4" each to arrive at the correct configuration. For the case of an 8' railing that results in an extended railing of length 98 1/2". Each spacing is a maximum of 4" and 98.5/4 = 24.625. Thus there must be at least 24.625 spaces between the spindles. Since the number of spaces must be an integer there must be at least 25 spaces and thus 26 spindles. The distance between the center of the spindles is then 98.5/25 = 3.94".
Cheers,Penny