# Speed, Distance and Time

**Speed, Distance and Time**

Speed, distance, and time are essential concepts in quantitative ability and are often used in various mathematical problems and real-life situations. Understanding these concepts helps in solving a wide range of quantitative problems involving motion, such as those related to trains, cars, boats, aeroplanes, and more.

**Speed:**

It is the rate at which an object covers a certain distance in a given amount of time. It is usually measured in units like metres per second (m/s), kilometres per hour (km/h), miles per hour (mph), etc. The formula to calculate speed is:

Speed of an object (S) = Distance to be covered by an object (D) / Time taken by an object (T)

**Distance:**

Distance is the length between two points, often measured in metres (m), kilometres (km), miles (mi), etc. In problems involving speed and time, you may be given the distance and asked to find either the speed or the time taken to cover that distance.

**Time:**

Time is the duration taken to cover a certain distance at a given speed. It is measured in seconds (s), minutes (min), hours (h), etc. The formula to calculate time is:

Time taken by an object (T) = Distance to be covered by an object (D) / Speed of an object (S)

**Common Problem Types**:

**Finding Speed:** Given the distance and time taken to cover that distance, you can find the speed using the formula: Speed of an object (S) = Distance to be covered by an object (D) / Time taken by an object (T)

**Finding Distance:** If you know the speed and the time taken to cover a certain distance, you can find the distance using the formula: Distance (D) = Speed (S) × Time (T).

**Finding Time:** If you know the speed and the distance covered, you can find the time taken to cover that distance using the formula: Time (T) = Distance (D) / Speed (S).

**Example 1**:

Let's say a car travels a distance of 300 kilometres in 5 hours. We use,

Speed of the car (S) = Distance to be covered by the car (D) / Time taken by the car (T)

S = 300 km/5 hours

S = 60 km/h

So, the speed of the car is 60 kilometres per hour.

**Example 2**:

A train travels a distance of 240 kilometres in 4 hours. What is the speed of the train?

Solution:

Speed of a train (S) = Distance travelled by the train (D) / Time taken by the train (T)

S = 240 km/4 hours

S = 60 km/h

Answer: The speed of the train is 60 kilometres per hour.

**Example 3:**

A boat travels at a speed of 25 knots and covers a distance of 150 nautical miles. How long will it take the boat to cover this distance?

Solution:

Time taken by the boat (T) = Distance covered by the boat (D) / Speed of the boat (S)

T = 150 nautical miles / 25 knots

T = 6 hours

Answer: It will take the boat 6 hours to cover a distance of 150 nautical miles.

These concepts are widely used in various quantitative ability and aptitude tests. Understanding how to apply them can help you solve problems efficiently and accurately. Practise with different types of speed, distance, and time problems to improve your skills in this area.