Study Guide & Educational Overview
### Key Word Problem Frameworks:
* **Motion & Travel**:
* Distance = Speed $\times$ Time ($d = vt$).
* Average speed for equal distance legs is the harmonic mean: $v_{\text{avg}} = \frac{2 v_1 v_2}{v_1 + v_2}$.
* **Collaborative Work Rates**:
* If Person A takes $T_a$ and Person B takes $T_b$: Combined Rate = $\frac{1}{T_a} + \frac{1}{T_b} = \frac{1}{T_{\text{together}}}$.
* **Commercial Arithmetic & Discounts**:
* Percentage markup/discount applied sequentially: $P_{\text{final}} = P_{\text{orig}} \times (1 + r_1) \times (1 - r_2)$.
* Simple Interest: $I = P \times r \times t$.
* **Proportions & Mixtures**:
* Ratio sharing: Divide total amount by sum of ratio parts, then multiply by each individual part.
* **Motion & Travel**:
* Distance = Speed $\times$ Time ($d = vt$).
* Average speed for equal distance legs is the harmonic mean: $v_{\text{avg}} = \frac{2 v_1 v_2}{v_1 + v_2}$.
* **Collaborative Work Rates**:
* If Person A takes $T_a$ and Person B takes $T_b$: Combined Rate = $\frac{1}{T_a} + \frac{1}{T_b} = \frac{1}{T_{\text{together}}}$.
* **Commercial Arithmetic & Discounts**:
* Percentage markup/discount applied sequentially: $P_{\text{final}} = P_{\text{orig}} \times (1 + r_1) \times (1 - r_2)$.
* Simple Interest: $I = P \times r \times t$.
* **Proportions & Mixtures**:
* Ratio sharing: Divide total amount by sum of ratio parts, then multiply by each individual part.
Frequently Asked Questions
Because the percentage is applied to a different base: $100 \times 0.80 = 80$, and $80 \times 1.20 = 96$, leaving a net 4% loss.
Yes! The in-game Options modal allows toggling timed mode, zen mode, sound effects, and question counts.
