Math Problems on Speed and Growth

Relative Speed and Distance

• The speed of an object relative to another object is the difference in their speeds.
• When objects are traveling in the same direction, their relative speed is calculated by subtracting the speed of the slower object from the speed of the faster object.
• If you need to find how far one object will travel before it catches up to another object traveling in the same direction, then divide the distance between the two objects by their relative speed.
• When objects are traveling in opposite directions, their relative speed is the sum of their speeds.
• If you need to find how far one object will travel before it meets another object moving in the opposite direction, then divide the total distance between the two objects by their relative speed.

Rates and Time

• When calculating the rates of change for two different entities that have a starting point with a difference in magnitude, then the concept of relative rates is used.
• The difference in the rates of change of the activities is the relative rate at which they are changing,
• To calculate the time at which the two entities reach the same point, divide the initial difference by the relative rate of change.

### Time and Distance

• To find the time it takes for objects to meet:
  • Divide the relative distance by the relative speed when they are traveling in opposite directions.
  • Divide the difference in distance by the relative speed when they are traveling in the same direction, and the faster object is overtaking the slower object.
  • Divide the total distance by the relative speed when they are traveling in the same direction, and the slower object needs to catch up to the faster object.
• The distance traveled by the object is the value of its speed multiplied by the time traveled.