Question

Elvira and Aletheia live $3.1$miles apart on the same street. They are in a study group that meets at a coffee shop between their houses. It took Elvira half an hour and Aletheia two-thirds of an hour to walk to the coffee shop. Aletheia’s speed is $0.6$miles per hour slower than Elvira’s speed. Find both women’s walking speeds.

Short answer

The walking speed of Elvira is$3miles/hr$and the walking speed of Aletheia is$2.4miles/hr$.

Step-by-step solution

Step 1. Given the information.

Distance $=3.1miles$.

Time for Elvira$=0.5hours$.

Time for Aletheia$=\frac{2}{3}hours$

Step 2. Assumptions

Let the speed of Elvira be $xmiles/hr$.

Then, the speed of Aletheia is $(x-0.6)miles/hr$.

We know, $Speed=\frac{Dis\tan ce}{Time}$.

Distance traveled by Elvira is $\frac{x}{2}miles$.

Distance traveled by Aletheia is$\frac{2}{3}(x-0.6)miles$.

Step 3. Solving the equations.

The equation according to the problem is,

$$\begin{gathered} \frac{x}{2}+\frac{2}{3}(x-0.6)=3.1 \\ \frac{x}{2}+\frac{2x}{3}-0.4=3.1 \\ \frac{3x+4x}{6}=3.5 \\ \frac{7x}{6}=3.5 \\ x=3.5\times \frac{6}{7} \\ x=3 \end{gathered}$$

The walking speed of Elvira is $3miles/hr$.

$$\begin{gathered} x-0.6=3-0.6 \\ =2.4 \end{gathered}$$

The walking speed of Aletheia is$2.4miles/hr$.