Question

k, averaging 12 miles per hour. on her way home she averages 8 takes one hour, how far does she live from her work? fill out the distance column. c = d = x mi 12 mi 1 mi distance rate time t c 12 r home d 8 done

Explanation:

Step1: Recall the distance - rate - time formula

The formula is $d = rt$ (distance = rate×time). Let the distance to work be $d$. The time taken to go to work, $t_1=\frac{d}{12}$ (since rate $r_1 = 12$ mph), and the time taken to return home, $t_2=\frac{d}{8}$ (since rate $r_2 = 8$ mph).

Step2: Set up an equation based on total time

The total time $t_1 + t_2=1$ hour. Substituting the expressions for $t_1$ and $t_2$ into the equation, we get $\frac{d}{12}+\frac{d}{8}=1$.

Step3: Find a common denominator

The common denominator of 12 and 8 is 24. Rewrite the left - hand side of the equation: $\frac{d\times2}{12\times2}+\frac{d\times3}{8\times3}=1$, which simplifies to $\frac{2d}{24}+\frac{3d}{24}=1$, or $\frac{2d + 3d}{24}=1$.

Step4: Combine like terms and solve for $d$

Combining like terms gives $\frac{5d}{24}=1$. Multiply both sides of the equation by 24 to get $5d=24$. Then divide both sides by 5, so $d = 4.8$ miles.

Answer:

4.8 miles