A train travels at a speed of 60km/h for 0.52h, of 30km/h for the next 0.24h, and then at 70km/h for the next 0.71h. What is the average speed of the train?
Time, speed, and distance are related using the equation: Distance = Speed × Time.
Answer: The average speed of the train is 59.93 km/h.
To find the average speed we need to use the relation:
Average speed = Total distance traveled/ Total time taken
Let's find the total distance traveled and the total time taken by the train.
To find the total distance traveled, let's find each distance first:
First speed = 60 km/h
Time for which the train moved at the first speed = 0.52 h
The first distance = Speed × Time
= 60 × 0.52 = 31.2 km
Second speed = 30 km/h
Time for which the train moved at the second speed = 0.24 h
The second distance = Speed × Time
= 30 × 0.24 = 7.2 km
Third speed = 70 km/h
Time for which the train moved at the third speed = 0.71 h
The third distance = Speed × Time
= 70 × 0.71 = 49.7 km
The total distance travelled = 31.2 km + 7.2 km + 49.7 km = 88.1 km
Total time taken = 0.52 h + 0.24 h + 0.71 h = 1.47 h
Now, Average speed = Total distance traveled/ Total time taken
or, Average speed = 88.1/1.47 ≈ 59.93 km/h