Math Problem Statement

Two cars start from the same point and travel in opposite directions. Car A travels at 50 mph and Car B travels at 60 mph. After 3 hours, how far apart are the cars?

Solution

The two cars are traveling in opposite directions, so the distance between them increases by the sum of their speeds.

  • Car A travels at 50 mph.
  • Car B travels at 60 mph.

After 3 hours:

  • Distance covered by Car A = 50mph×3hours=150miles50 \, \text{mph} \times 3 \, \text{hours} = 150 \, \text{miles}.
  • Distance covered by Car B = 60mph×3hours=180miles60 \, \text{mph} \times 3 \, \text{hours} = 180 \, \text{miles}.

Now, since they are traveling in opposite directions, the total distance between them is the sum of these distances:

Total distance=150miles+180miles=330miles\text{Total distance} = 150 \, \text{miles} + 180 \, \text{miles} = 330 \, \text{miles}

So, after 3 hours, the cars are 330 miles apart.

Would you like more details or have any questions?


Here are 5 related questions:

  1. What if Car A traveled at 40 mph instead of 50 mph?
  2. How far apart would they be after 5 hours?
  3. If they started 10 miles apart, how would the result change?
  4. What if Car B traveled for 4 hours and Car A for only 3 hours?
  5. How would their distance change if both cars slowed down by 10 mph after 1 hour?

Tip: When two objects move in opposite directions, you can find the total distance by adding their individual distances.

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Math Problem Analysis

Mathematical Concepts

Speed and Distance
Addition of Distances
Linear Motion

Formulas

Distance = Speed × Time

Theorems

Relative Speed Theorem for Opposite Directions

Suitable Grade Level

Grades 5-7