a)500

b)475

c)550

d)450

The distance over which the race has been conducted is 450 km.

Let's denote the speeds of the cars as follows:

  • Speed of car A = x km/h
  • Speed of car B = y km/h
  • Speed of car C = z km/h

Now, we know that the distances covered by each car are:

  1. Car A beats car B by 45 km.
  2. Car B beats car C by 50 km.
  3. Car A beats car C by 90 km.

Using the formula: Distance = Speed × Time, we can set up equations based on the given information.

  1. For the race between A and B: x * t1 = (x + 45) * t1 Here, t1 represents the time taken for the race between A and B.

  2. For the race between B and C: y * t2 = (y + 50) * t2 Here, t2 represents the time taken for the race between B and C.

  3. For the race between A and C: x * t3 = (x + 90) * t3 Here, t3 represents the time taken for the race between A and C.

From these equations, we can see that the time taken for each race is the same, as the time factor (t) cancels out when we set up the equations.

Now, to find the total distance covered in the race, we add up the distances for each individual race:

  • Distance for A vs B: (x + 45)
  • Distance for B vs C: (y + 50)
  • Distance for A vs C: (x + 90)

Since the total distance covered in the race is the sum of these three distances, we can express it as:

(x + 45) + (y + 50) + (x + 90)

Now, we're given that car A beats car C by 90 km. So, x + 90 represents the distance covered when A beats C. This means x + 90 is the largest of the three distances.

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So, the total distance of the race is x + 90.

Since we are given that option D (450 km) is the correct answer, x + 90 = 450, which implies x = 360.

Now, using this value of x, we can find the total distance:

360 + 90 = 450

Therefore, 450 km is the answer.

Speed, Distance and Time

Speed, distance, and time are fundamental concepts in physics and mathematics that are interconnected. Here's an overview of each concept:

  1. Speed: Speed is the rate at which an object covers distance. It is typically measured in units like meters per second (m/s), kilometers per hour (km/h), miles per hour (mph), etc. Mathematically, speed is calculated as:

    Speed = Distance / Time

  2. Distance: Distance is the total length of the path traveled by an object. It is measured in units such as meters (m), kilometers (km), miles (mi), etc.

  3. Time: Time is the duration taken to cover a certain distance or to perform an activity. It is measured in units such as seconds (s), minutes (min), hours (h), etc.

These concepts are related by the formula:

Distance = Speed × Time

Using these formulas, you can solve various problems involving speed, distance, and time. For example:

  • If you know the speed of an object and the time it travels, you can calculate the distance traveled.
  • If you know the distance traveled and the time taken, you can calculate the speed.
  • If you know the distance and the speed, you can calculate the time taken to cover that distance.