Question

A new obstacle course is home to several new types of challenging obstacles. One such obstacle is traversing a 15-stair staircase. To make it more challenging, the stairs are not uniformly spaced. Rather, the vertical space between consecutive stairs for the first 10 stairs is 1 1/3 feet and the vertical space for the last 5 stairs is 1 3/4 feet. What is the total vertical distance traveled ascending and descending the entire 15-stair staircase?

Answer 1

Answer: $22\frac{1}{2}\text{ Feet}$

Step-by-step explanation:

Here, the vertical space between two consecutive stairs in first 10 stairs = $1\frac{1}{3}\text{ feet}$

⇒ The total vertical distance for 10 stairs = $10\times 1\frac{1}{3}=10\times \frac{4}{3}=\frac{40}{3}\text{ feet}$

Also, The vertical space between two consecutive stairs for last 5 stairs = $1\frac{3}{4}\text{ feet}$

⇒ The total vertical distance for 10 stairs = $10\times 1\frac{1}{3}=5\times \frac{7}{4}=\frac{35}{4}\text{ feet}$

Thus, The total vertical distance = Total vertical space for the first 10 stairs + Total vertical space for the last 5 stairs

= $\frac{40}{3} + \frac{35}{4}$

= $\frac{160+105}{12}$

= $\frac{265}{12}$

= $22\frac{1}{2}\text{ Feet}$