Question

marcos sister is driving home from college. along the way, she drives at the speed limit on an interstate highway and then on a u.s. highway. this equation describes the number of miles, y, that she drives on the interstate highway in x hours: y = 65x this graph shows the distance she travels on the u.s. highway over time: u.s. highway graph of u.s. highway distance vs time with y-axis distance (miles) from 0 to 500 and x-axis time (hours) from 0 to 10 which highway has a faster speed limit? the interstate highway the u.s. highway how far can marcos sister drive on that highway in 3 hours? miles

Explanation:

Part 1: Which highway has a faster speed limit?

To determine the speed on each highway, we use the formula \( \text{speed} = \frac{\text{distance}}{\text{time}} \) (or from the equation \( y = mx \), where \( m \) is the slope, representing speed).

• Interstate Highway: The equation is \( y = 65x \), so the speed (slope) is \( 65 \) miles per hour.
• U.S. Highway: From the graph, when \( x = 5 \) hours, \( y = 300 \) miles. Using \( \text{speed} = \frac{y}{x} \), we get \( \frac{300}{5} = 60 \) miles per hour.

Since \( 65 > 60 \), the interstate highway has a faster speed limit.

Step1: Use the interstate highway’s equation \( y = 65x \).

We know \( x = 3 \) hours. Substitute \( x = 3 \) into the equation.

Step2: Calculate \( y \).

\( y = 65 \times 3 = 195 \).

Answer:

the interstate highway

Part 2: How far can Marco’s sister drive on that highway (interstate) in 3 hours?