Question

Two cars start 25 miles apart and drive away from each other in opposite directions at speeds of 50 and 70 miles per hour. In approximately how many minutes will they be 400 miles apart?

• A. 200
• B. 3.33
• C. 187.5
• D. None of the other answers
• E. 3.125

Hint:

In relative speed problems, remember: if objects move in opposite directions, add their speeds. If they move in the same direction, subtract the slower speed from the faster speed. Pay close attention to the units (hours vs. minutes) requested in the answer.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a relative speed problem. When two objects move in opposite directions, their relative speed is the sum of their individual speeds. This relative speed represents how quickly the distance between them is increasing.
Step 2: Key Formula or Approach:
1. Calculate the relative speed of the two cars.
2. Determine the additional distance the cars need to be apart.
3. Use the formula: Time = Distance / Speed.
4. Convert the time from hours to minutes.
Step 3: Detailed Explanation:
The speeds of the two cars are 50 mph and 70 mph. Since they are moving in opposite directions, their relative speed is the sum of their speeds: \[ \text{Relative Speed} = 50 \, \text{mph} + 70 \, \text{mph} = 120 \, \text{mph} \] The cars start 25 miles apart and need to be 400 miles apart. The additional distance they need to cover is: \[ \text{Distance} = 400 \, \text{miles} - 25 \, \text{miles} = 375 \, \text{miles} \] Now, we can calculate the time it will take to cover this distance at their relative speed: \[ \text{Time (in hours)} = \frac{\text{Distance}}{\text{Speed}} = \frac{375 \, \text{miles}}{120 \, \text{mph}} \] \[ \text{Time (in hours)} = \frac{375}{120} = \frac{75}{24} = \frac{25}{8} \, \text{hours} \] The question asks for the time in minutes. We convert hours to minutes by multiplying by 60: \[ \text{Time (in minutes)} = \frac{25}{8} \times 60 = \frac{1500}{8} = \frac{750}{4} = \frac{375}{2} \] \[ \text{Time (in minutes)} = 187.5 \] Step 4: Final Answer:
It will take 187.5 minutes for the cars to be 400 miles apart.