Question

celeste rides her bike to work, averaging 12 miles per hour. on her way home she averages 8 miles per hour. if the total trip takes one hour, how far does she live from her work? fill out the rate column in the table below. a = b =

distance	rate	time
return home	b

done

Explanation:

Step1: Identify the rates

The rate to work is 12 miles per hour and rate back home is 8 miles per hour. So $a = 12$ and $b=8$.

Step2: Let the distance to work be $d$ miles.

The time taken to work $t_1=\frac{d}{12}$ (using the formula $t=\frac{d}{r}$, where $t$ is time, $d$ is distance and $r$ is rate). The time taken to return home $t_2=\frac{d}{8}$.

Step3: Use the total - time information

The total time for the round - trip is 1 hour. So $t_1 + t_2=1$, which means $\frac{d}{12}+\frac{d}{8}=1$.

Step4: Find a common denominator

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

Step5: Simplify the equation

$\frac{5d}{24}=1$. Multiply both sides by 24 to get $5d = 24$. Then divide both sides by 5 to find $d=\frac{24}{5}=4.8$ miles.

Answer:

$a = 12$, $b = 8$, distance to work is 4.8 miles.