To determine the correct equation for finding the time, [tex]\( h \)[/tex], it will take for the distance between the train and the railroad marker to be 4 miles, we need to express the relationship between distance, speed, and time.
1. Given Information:
- The train's initial distance from the marker: 200 miles.
- The train's speed: 65 miles per hour.
- The final distance between the train and the marker: 4 miles.
2. Distance Equation:
- The formula for distance is:
[tex]\[
\text{Distance} = \text{Initial Distance} - (\text{Speed} \times \text{Time})
\][/tex]
- Let [tex]\( h \)[/tex] be the time in hours.
3. Set Up the Equation:
- Initially, the train is 200 miles away from the marker.
- After traveling for [tex]\( h \)[/tex] hours at a speed of 65 miles per hour, the train will cover [tex]\( 65h \)[/tex] miles.
- The remaining distance to the marker can be expressed as:
[tex]\[
200 - 65h
\][/tex]
- We need this remaining distance to be 4 miles, either approaching or passing the marker. Therefore, we set up the absolute value equation:
[tex]\[
|200 - 65h| = 4
\][/tex]
4. Conclusion:
- The equation that correctly represents the scenario is [tex]\( |200 - 65 h| = 4 \)[/tex].
Thus, the correct answer is:
C. [tex]\( |200-65 h|=4 \)[/tex]
