lupe can ride her bike at a rate of 20 mph when there is no wind. on one particular day, she rode 2 miles…

Explanation:

Step1: Set up the time - rate equations

Let the speed of the wind be $w$ mph. The speed against the wind is $(20 - w)$ mph and the speed with the wind is $(20 + w)$ mph. Since time $t=\frac{d}{r}$ (where $d$ is distance and $r$ is rate), and the time against the wind $t_1$ for a distance $d_1 = 2$ miles and the time with the wind $t_2$ for a distance $d_2=3$ miles are equal. So, $\frac{2}{20 - w}=\frac{3}{20 + w}$.

Step2: Cross - multiply

Cross - multiplying the equation $\frac{2}{20 - w}=\frac{3}{20 + w}$ gives us $2(20 + w)=3(20 - w)$.

Step3: Expand both sides

Expand the left - hand side: $2\times20+2w = 40 + 2w$, and the right - hand side: $3\times20-3w=60 - 3w$. So the equation becomes $40 + 2w=60 - 3w$.

Step4: Solve for $w$

Add $3w$ to both sides: $40 + 2w+3w=60 - 3w+3w$, which simplifies to $40 + 5w=60$. Then subtract 40 from both sides: $5w=60 - 40$, so $5w = 20$. Divide both sides by 5: $w=\frac{20}{5}=4$ mph.

Answer:

A. 4 mph