A and B take part in a 100 m race. A runs at 5 km per hour. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is

B's speed is 4.14 km/h.

Let's find B's speed:

1. Convert A's speed to m/s:

  • 5 km/h * (5/18) m/s/km = 25/18 m/s

2. Find the time A takes to finish:

  • Distance / Speed = 100 m / (25/18) m/s = 72 seconds

3. Find the distance B needs to cover:

  • 100 m (total distance) - 8 m (head start) = 92 m

4. Find the time B takes to finish (including head start):

  • A's time + head start time = 72 seconds + 8 seconds = 80 seconds

5. Calculate B's speed:

  • Distance / Time = 92 m / 80 seconds = 1.15 m/s

6. Convert B's speed to km/h:

  • 1.15 m/s * (18/5) km/h/m/s = 4.14 km/h

Therefore, B's speed is 4.14 km/h.

Distance, Speed and Time in Mathematics

Distance (D): Distance refers to the total length of the path traveled by an object. It is usually measured in units like meters (m), kilometers (km), miles (mi), etc.

Article continues below advertisement

Article continues below advertisement

Speed (S): Speed is the rate at which an object covers distance. It's defined as the distance traveled per unit of time. Mathematically, it's expressed as:

Speed (S) = Distance (D) / Time (T)

Time (T): Time represents the duration taken to travel a certain distance at a given speed. It is usually measured in units such as seconds (s), minutes (min), hours (h), etc.

These three quantities are interrelated through the formula:

D = S * T

This formula, often referred to as the "distance formula," demonstrates that distance equals speed multiplied by time. You can rearrange this formula to solve for any of the three variables depending on what information is given and what you're trying to find.

For example:

  • If you know the speed and time, you can find the distance traveled.
  • If you know the distance and speed, you can find the time taken.
  • If you know the distance and time, you can find the speed.

Here are some common formulas derived from the basic equation, D = S * T:

  1. S = D / T (To find speed)
  2. T = D / S (To find time)

These concepts are extensively used in various fields such as physics, engineering, navigation, and everyday life problem-solving. Understanding their relationships helps in solving problems involving motion, travel, and speed efficiently.