Question

hannah runs down the street to catch her bus. she runs for a total of 12 seconds. on the sidewalk, she runs 16 feet per second. when she crosses the street, she runs 3 feet per second. hannah runs a total distance of 127 feet. how many seconds did hannah spend running on the sidewalk? enter your answer in the box.

Explanation:

Step1: Define variables

Let \( x \) be the seconds Hannah spent running on the sidewalk. Then the seconds she spent running across the street is \( 12 - x \).

Step2: Set up distance equation

Distance on sidewalk: \( 16x \) feet. Distance across street: \( 3(12 - x) \) feet. Total distance is 127 feet, so:
\[ 16x + 3(12 - x) = 127 \]

Step3: Simplify the equation

Expand and combine like terms:
\[ 16x + 36 - 3x = 127 \]
\[ 13x + 36 = 127 \]

Step4: Solve for \( x \)

Subtract 36 from both sides:
\[ 13x = 127 - 36 \]
\[ 13x = 91 \]
Divide by 13:
\[ x = \frac{91}{13} = 7 \]

Answer:

7