Speed Distance and Time

Suppose an Express train leaves the station A at 0900 hours. It runs nonstop and reaches the station B at 1100 hours. So the Express train take 2 hours to cover the distance. A Mail train covers the distance between these stations in 3 hours. If the distance between the two stations is 120 km, which train travels faster?

To find this, we use the unitary method.

The distance covered by the Express train in 2 hours = 120 km

The distance covered by the Express train in 1 hour = \(\frac{120}{2}\) km = 60 km

The distance covered by the Mail train in 3 hours = 120 km

The distance covered by the Mail train in 1 hour = \(\frac{120}{3}\) km = 40 km

So, the Express train travels more distance than the Mail train in 1 hour. Hence, the Express train travels faster than the Mail train. We say that the Express train has greater speed than the Mail train.

Speed: The distance travelled by a body or vehicle in a unit time is known as its speed.

Speed = \(\frac{\textrm{Distance (in unit of length)}}{\textrm{Time (in unit of time)}}\)

Average Speed: The total distance covered by a body divided by the total time taken by the body is known as average speed.

Average Speed = \(\frac{\textrm{Total distance travelled}}{\textrm{Total Time Taken}}\)

and

Speed = \(\frac{\textrm{Total Distance Covered}}{\textrm{Total time taken-time of stoppage}}\)

= \(\frac{\textrm{Distance}}{\textrm{Time}}\)

If there is no stoppage, that is, the time of stoppage is zero, the average speed equals the speed.

Solved examples on speed distance and time:

1. Nancy travelled a distance of 455 km by car in 10 hours. Find the speed of the car.

Distance travelled by car = 455 km

Time taken = 10 hours

Therefore, speed = \(\frac{\textrm{Distance}}{\textrm{Time}}\)

= \(\frac{455}{10}\) km/hr

= 45.5 km per hour

2. Find the speed and average speed of a train which leaves Madras at 1 p.m. and reaches Vijayawada in the same day at 9 p.m. The distance between the two stations is 432 km and the total time for stoppage is 2 hours between these stations.

Total time taken = 9 -1, that is, 8 hours;

Time of stoppage = 2 hours, that is, actual time taken = 8 hours - 2 hours = 6 hours

Speed = \(\frac{\textrm{Distance}}{\textrm{Time}}\)

= \(\frac{432 km}{6 hr}\)

= \(\frac{432}{6}\)

= 72 km/hr

Average speed = \(\frac{\textrm{Total Distance}}{\textrm{Total Time}}\)

= \(\frac{432}{8}\) km/hr

= 54 km/hr

3. A car travels a distance of 595 km in 8 ½ hours. What is its speed?

Distance travelled = 595 km

Time taken to travel this distance = 8\(\frac{1}{2}\) hours = \(\frac{17}{2}\) hours