Question

Determine whether you need an estimate or an exact answer. Then solve.

Luis rode his bike 1.2 miles to his friend's house, then 0.7 miles to the video store, then 1.9 miles to the library. If he rode the same route back home, how far did he travel in all?

Short answer

Luis traveled a total of 7.6 miles to reach the final destination and come back from there by following the same routes.

Step-by-step solution

Step 1. The distance traveled Luis by his bike.

$\begin{array}{l}\text{Distancetravelledtohisfriend'shouse}{d}_1=1.2\text{miles}\\ \text{Distancetravelledfromfriend'shousetovideostore}{d}_2=0.7\text{miles}\\ \text{Distancetravelledfromvideostoretolibrary}{d}_3=1.9\text{miles}\end{array}$

Step 2. Applying the summation rule.

Calculate the distance traveled by Luis to reach the library.

$\begin{array}{l}{D}_1=d_1+d_2+d_3\\ D_1=1.2+0.7+1.9\\ D_1=3.8\end{array}$

Step 3. Applying the summation rule again.

Calculate the distance traveled by Luis to come back via the same route.

$\begin{array}{l}{D}_2=d_3+d_2+d_1\\ D_2=1.9+0.7+1.2\\ D_2=3.8\end{array}$

Step 4. Evaluate the total distance.

$\begin{array}{l}D=D_1+D_2\\ D=3.8+3.8\\ D=7.6\end{array}$

Therefore, the total distance traveled by Luis for both routes is 7.6 miles.