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A train travels at $60 km/h$ for $0.52h$, at $30 km/h$ for the next $0.24h$ and at $70 km/h$ for the next $0.71h$. What is the average speed of the train?
A. $125km/h$
B. $10 km/h$
C. $20 km/h$
D. $59.9 km/h$

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Last updated date: 20th Jun 2024
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Answer
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Hint:The average speed of the train is given by the total distance travelled by train divided by the total time taken by it to travel that distance. We have to find the distance travelled in various time periods and then calculate the average speed by the before mentioned formula.

Complete step by step answer:
Average speed is actually the speed that an object needs to travel at so as to cover the same total distance in the same time that it did at different speeds for different time periods.
We have to calculate the total distance travelled by train in various time periods.

In the first case, the train travels at a speed of 60 km/h for 0.52hr
Now, speed = distance/time=60km/h
Distance= $60 \times 0.52 = 31.2km$

In the second case, the train travels at a speed of 30km/h for 0.24hr
Distance= $30 \times 0.24 = 7.2km$

In the third case, the train travels at a speed of 70km/h for a time of 0.71 hr, so
Distance= $70 \times 0.71 = 49.7km$

Now, we get the total distance travelled as,
$\Rightarrow 31.2 + 7.2 + 49.7 = 88.1km$

Also, we can get the total of travel as
$\Rightarrow0.52 + 0.24 + 0.71 = 1.47hr$

So, the average speed can be calculated now as,
Average speed = Total distance travelled / Total time taken
$\therefore v = \dfrac{{88.1km}}{{1.47hr}} = 59.9km/hr$

Therefore, the correct answer is option D.

Note:The units can also be converted to m/s and solved, that is however the options demand. Here, because all the options are in km/h , we needn’t convert the units. Also, we have to note that the average speed isn’t simply the average of all speeds, which is a common mistake made by students.