Question

solution
neva is training for a race. this week, she bikes 5.5 times as far as she runs. her total distance running and biking this week is 26 mi. how far does neva run this week? show your work.

Explanation:

Step1: Define variables

Let \( r \) be the distance Neva runs (in miles) and \( b \) be the distance she bikes (in miles). We know that \( b = 5.5r \) (she bikes 5.5 times as far as she runs) and \( r + b=26 \) (total distance running and biking is 26 miles).

Step2: Substitute \( b \) into the total distance equation

Substitute \( b = 5.5r \) into \( r + b = 26 \). We get \( r+5.5r = 26 \).

Step3: Combine like terms

Combine \( r \) and \( 5.5r \): \( 6.5r=26 \).

Step4: Solve for \( r \)

Divide both sides by 6.5: \( r=\frac{26}{6.5} = 4 \).

Answer:

Neva runs 4 miles this week.