Question

construct a table for a distance - rate - time problem
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 = 12 mph
b = 8mph
fill out the distance column.
c =
d =
distance rate time
to work c 12
return home d 8
distance rate time
to work a
return home b

Explanation:

Step1: Let the distance to work be $d$.

Since the distance to work and the distance back home is the same, $c = d$.

Step2: Use the formula $t=\frac{d}{r}$ (where $t$ is time, $d$ is distance and $r$ is rate).

The time taken to go to work $t_1=\frac{d}{12}$, and the time taken to return home $t_2=\frac{d}{8}$.

Step3: Set up an equation based on total - time.

We know that $t_1 + t_2=1$ hour. So, $\frac{d}{12}+\frac{d}{8}=1$.

Step4: Find a common denominator.

The common denominator of 12 and 8 is 24. Rewrite the left - hand side: $\frac{2d}{24}+\frac{3d}{24}=1$, which simplifies to $\frac{2d + 3d}{24}=1$ or $\frac{5d}{24}=1$.

Step5: Solve for $d$.

Multiply both sides of the equation by 24 to get $5d = 24$, then $d=\frac{24}{5}=4.8$ miles.

Answer:

$c = 4.8$ miles, $d = 4.8$ miles