A train travels the first 15 km at a uniform speed of 30 km/h; the next 75 km at a uniform speed of 50 km/h; and the last 10 km at a uniform speed of 20 km/h. Calculate the average speed for the entire train journey.

Uniform Speed

Uniform speed refers to the constant rate at which an object moves, covering equal distances in equal intervals of time. In other words, when an object maintains a consistent speed throughout its motion, it is said to be moving at a uniform speed.

Uniform speed is often associated with linear motion, such as an object moving along a straight line. It does not consider any variations or changes in speed that may occur during the motion.

Average Speed

Average speed refers to the overall rate at which an object or person covers a certain distance over a given period of time. It is calculated by dividing the total distance traveled by the total time taken.

Average speed provides a measure of the overall rate of motion, taking into account both the distance covered and the time taken. It gives an indication of how fast, on average, an object or person is moving over a specific journey or time interval.

Solution

To calculate the average speed for the entire train journey, we need to find the total distance traveled and the total time taken.

First, let’s calculate the time taken for each segment of the journey using the formula Time = Distance / Speed.

For the first segment:

Time taken = Distance / Speed = 15 km / 30 km/h = 0.5 hours

For the second segment:

Time taken = Distance / Speed = 75 km / 50 km/h = 1.5 hours

For the third segment:

Time taken = Distance / Speed = 10 km / 20 km/h = 0.5 hours

Now, let’s calculate the total distance traveled:

Total distance = 15 km + 75 km + 10 km = 100 km

To calculate the total time taken, we sum up the individual times:

Total time = 0.5 hours + 1.5 hours + 0.5 hours = 2.5 hours

Finally, we can calculate the average speed using the formula Average Speed = Total Distance / Total Time:

Average Speed = 100 km / 2.5 hours = 40 km/h

Therefore, the average speed for the entire train journey is 40 km/h.

Summary

A train travels the first 15 km at a uniform speed of 30 km/h; the next 75 km at a uniform speed of 50 km/h; and the last 10 km at a uniform speed of 20 km/h. Calculate the average speed for the entire train journey.

A train travels the first 15 km at a uniform speed of 30 km/h; the next 75 km at a uniform speed of 50 km/h; and the last 10 km at a uniform speed of 20 km/h. The average speed for the entire train journey is 40 km/hr.

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