Calculate the Ladder Height: Using 0.036 m/s Average Speed Over Sequential Activities

To solve Carmen's problem, let's go through each step methodically:

• Step 1: Calculate the total time taken
  • Climbing time: $90$ seconds
  • Pause time: $15$ seconds
  • Slide down time: $20$ seconds
  Total time: $90 + 15 + 20 = 125 \text{ seconds}$
• Step 2: Use the average speed formula to set up an equation
  • Average speed given is $0.036$ meters/second.
  Let the height of the ladder be $h$. Total distance traveled, from the base of the ladder to the end of the slide, is the sum of the height of the ladder and the slide length: $\text{Total distance} = h + 3$ The average speed equation becomes: $0.036 = \frac{h + 3}{125}$
• Step 3: Solve for the height $h$ $0.036 \times 125 = h + 3$ $4.5 = h + 3$ $h = 4.5 - 3 = 1.5 \text{ meters}$

Therefore, the height of the ladder is $1.5$ meters, which matches the correct answer choice.