Select the correct answer.

A train is moving at a rate of 65 miles/hour toward a railroad marker located 200 miles away. Which equation could be used to find the time it will take for the distance between the train and the railroad marker to be 4 miles, where [tex]h[/tex] represents the time in hours?

A. [tex]|4 + 65h| = 200[/tex]
B. [tex]|65 - 4h| = 200[/tex]
C. [tex]|200 - 65h| = 4[/tex]
D. [tex]|200 - 4h| = 65[/tex]



Answer :

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]