Use the diagram above to calculate the gradient of the ramp.

The gradient for a safe descending wheelchair ramp is $- \frac{1}{{12}}$.

Using your answer to part (a), comment on why wheelchair ramp ${\text{A}}$ is not safe.

The equation of a second wheelchair ramp, B, is $2x + 24y - 1920 = 0$.

(i)     Determine whether wheelchair ramp ${\text{B}}$ is safe or not. Justify your answer.

(ii)     Find the horizontal distance of wheelchair ramp ${\text{B}}$.

$- \frac{{80}}{{940}}{\text{ }}\left( {-0.0851, -0.085106 \ldots , -\frac{4}{{47}}} \right)$     (A1)     (C1)

[1 mark]

$-0.0851{\text{ }} (-0.085106 \ldots ) <  - \frac{1}{{12}}(-0.083333 \ldots )$     (A1)(ft)     (C1)

Notes: Accept “less than” in place of inequality.

     Award (A0) if incorrect inequality seen.

     Follow through from part (a).

[1 mark]

(i)     ramp ${\text{B}}$ is safe     (A1)

the gradient of ramp ${\text{B}}$ is $- \frac{1}{{12}}$     (R1)

Notes: Award (R1) for “the gradient of ramp ${\text{B}}$ is $- \frac{1}{{12}}$” seen.

     Do not award (A1)(R0).

(ii)     $2x = 1920$     (M1)

Note: Accept alternative methods.

$960 {\text{ (cm)}}$     (A1)     (C4)

[4 marks]