Problem
Andy walks $5.4 \mathrm{~km}$ in the same time that Dianne walks $4.2 \mathrm{~km}$. On average, Andy walks $0.5 \mathrm{~km} / \mathrm{h}$ faster than Dianne. 1. Determine the algebraic expression for the time it takes Andy to walk $5.4 \mathrm{~km}$. 2. Determine the algebraic expression for the time it takes Dianne to walk 4.2 $\mathrm{km}$. 3. What equation will be used to determine the walking speed of each walker? 4. What is the walking speed of both walkers, to the nearest tenth of a $\mathrm{km} / \mathrm{h}$ ?
Solution
Step 1 ：Let's denote Andy's speed as 'a'.
Step 2 ：Since time is calculated by dividing distance by speed, the time it takes Andy to walk 5.4 km can be represented as 5.4 divided by 'a'.
Step 3 ：Thus, the algebraic expression for the time it takes Andy to walk 5.4 km is \( \frac{5.4}{a} \).
Step 4 ：Final Answer: The algebraic expression for the time it takes Andy to walk 5.4 km is \( \boxed{\frac{5.4}{a}} \).
