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 = \(\frac{\textrm{Total Distance Covered}}{\textrm{Total time taken-time of stoppage}}\)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
Speed of the car = \(\frac{\textrm{Distance}}{\textrm{Time}}\)
= \(\frac{\frac{595}{17}}{2}\) km/hour
= \(\frac{592 × 2}{17}\)
= 70 km/hr
Therefore, the speed of the car = 70 km/hour.
Express Speed in Different Units
To find Speed when Distance and Time are given.
To find the Distance when Speed and Time are given.
To find Time when Distance and Speed are given.
Worksheet on Expressing Speed in Different Units
Worksheet on Speed, Distance and Time.
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5th Grade Math Problems
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