Question

after crossing a bridge, michael drives at a constant speed. the graph below shows the distance (in miles) versus the time (since michael crossed the bridge) (in hours).
use the graph to answer the questions.

(a) what is the distance traveled at 1 hour?
\\(\square\\) miles

(b) what is the distance traveled at 2 hours?
\\(\square\\) miles

(c) how much does the distance increase for each hour since michael crossed the bridge?

Explanation:

Step1: Determine the speed (slope of the line)

From the graph, we can see that when time \( t = 1 \) hour, the distance \( d \) seems to be 60 miles (assuming the grid lines: let's check the pattern. If at \( t = 0.5 \) hours, distance is 30 miles, then speed \( v=\frac{\text{distance}}{\text{time}}=\frac{30}{0.5} = 60 \) miles per hour. So the equation of the line is \( d = 60t \) (since it passes through the origin, \( d=vt \) with \( v = 60 \)).

Step2: Solve part (a) - distance at 10 minutes

First, convert 10 minutes to hours. Since 1 hour = 60 minutes, 10 minutes \(=\frac{10}{60}=\frac{1}{6}\) hours.
Using the formula \( d = 60t \), substitute \( t=\frac{1}{6} \):
\( d = 60\times\frac{1}{6}=10 \) miles.

Step3: Solve part (b) - distance at 1.5 hours

Using the formula \( d = 60t \), substitute \( t = 1.5 \):
\( d=60\times1.5 = 90 \) miles.

Step4: Solve part (c) - distance increase per hour

The speed is the rate of change of distance with respect to time. From the equation \( d = 60t \), the slope (which is speed) is 60. So the distance increases by 60 miles per hour.

Answer:

(a) 10 miles
(b) 90 miles
(c) 60 miles per hour