Question

A local diner must build a wheelchair ramp to provide handicap access to the restaurant. Building codes require that a wheelchair ramp must have a maximum rise of 1 in. for every horizontal distance of 12 in. (a) What is the maximum allowable slope for a wheelchair ramp? Assuming that the ramp has maximum rise, find a linear function H that models the height of the ramp above the ground as a function of the horizontal distance x? H(x) = (b) If the space available to build a ramp is 150 in. wide, how high does the ramp reach? in

Answer 1

(a) Maximum slope
`=\frac {1}{12}`,
`H(x)=\frac {1}{12}x`

(b) 12.5 in.

Explanation:

The given condition is the wheelchair ramp must have a maximum rise of 1 in. for every horizontal distance of 12 in.

(a) Let m be the maximum allowable slope for the ramp.

`m=\frac{\text{Maximum rise for the given horozontal disence}}{\text{The given horizontal distance}}`

`\Rightarrow m=(1)/(12)`.

Let x be the distance in the horizontal direction as shown in the figure.

So, for slope m, the linear function H for the height is

`H(x)=mx+C`, where C is constant.

Now, at the starting of the ramp, x=0, and H=0.

Putting this condition back to the equation, we have

`0=m* 0 +C`

`\Rightarrow C=0`.

Hence, the required equation is

`H(x)=\frac {1}{12}x`

(b) The ramp is 150 in. wide,

So, height gained by the ramp at the end is,

`H(x=150)=\frac {1}{12}* 150=12.5` in.