Question

7. John decides to walk down a set of steps. He also made the following observations
• At 1/4 way down, his eye-level was one step below the top
• At 3/7 way down, he was twice his eye-level down from the top
• At 1/2 way down, he eye-level was 0.4m above 1/3 the way down
How high was
• John
• Each step
The set of stairs

Answer 1

Answer on Question #85660 – Math – Algebra

Question

7. John decides to walk down a set of steps. He also made the following observations

- At 1/4 way down, his eye-level was one step below the top

- At 3/7 way down, he was twice his eye-level down from the top

- At 1/2 way down, he eye-level was 0.4m above 1/3 the way down

How high was

- John

- Each step

The set of stairs

Solution

The height of John = x

The height of the stairs = y

The height of the step = z

Make a system of equations

(1) $\left(y - \frac{1}{4} y\right) + x + z = y$

(2) $\left(y - \frac{3}{7} y\right) + 2x = y$

(3) $\left(y - \frac{1}{2} y\right) + x + \frac{1}{3} y - 0.4 = y$

Solve the system of two equations

(2) $\left(y - \frac{3}{7} y\right) + 2x = y \Rightarrow 2x = y - \frac{4}{7} y \Rightarrow x = \frac{3}{14} y$

(3) $\left(y - \frac{1}{2} y\right) + x + \frac{1}{3} y - 0.4 = y \Rightarrow \frac{1}{2} y + \frac{3}{14} y + \frac{1}{3} y - 0.4 = y \Rightarrow \frac{21 + 9 + 14}{42} - y = 0.4$

$$\begin{array}{l} \frac{1}{21} y = 0.4 \Rightarrow y = 8.4m \\ x = \frac{3}{14} y \Rightarrow x = 1.8m \\ \end{array}$$

Find the height of the step

(1) $\left(y - \frac{1}{4} y\right) + x + z = y \Rightarrow z = \frac{1}{4} y - x \Rightarrow z = 0.3m$

Answer: The height of John = 1.8m; The height of the stairs = 8.4m; The height of the step = 0.3m.

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