Question

A train travels at a speed of $60$ kilometres per hour for $0.52$ hour, at $30$ kilometres per hour for the next $0.24$ hour and then at $70$ kilometres per hour for the next $0.71$ hour. What is the average speed of the train?

Answer 1

Hint: If you need to answer these types of questions, then you need to be clear with the language. Unless and until you understand the question clearly, you will not be able to come up with a solution. In the question, we are given a word problem in which we are provided with different speeds of a train for different time periods. We calculate the distance by the train at each speed by using the formula ${\text{Distance = }}\,{\text{Speed}} \times {\text{Time}}$. We find the total time by adding up all the time periods. Then, we divide the total distance travelled by the total time taken to find the average speed of the train.

Complete answer: So, initial speed of train $ = 60$ kilometres per hour
Time of travel $ = 0.52$ hour
So, distance travelled in this time period is, ${\text{Distance = }}\,{\text{Speed}} \times {\text{Time}}$
$ \Rightarrow {\text{Distance = 60kmph}} \times {\text{0}}{\text{.52h}}$
\[ \Rightarrow {\text{Distance = }}\,{\text{31}}{\text{.2km}}\]
Now, speed of train $ = 30$ kilometres per hour
Time of travel $ = 0.24$ hour
So, distance travelled in this time period is, ${\text{Distance = }}\,{\text{Speed}} \times {\text{Time}}$
$ \Rightarrow {\text{Distance = }}\,30\,{\text{kmph}} \times {\text{0}}{\text{.24}}\,{\text{h}}$
\[ \Rightarrow {\text{Distance = }}\,7.2\,{\text{km}}\]
Also, in the last time period,
Speed of train $ = 70$ kilometres per hour
Time of travel $ = 0.71$ hour
So, distance travelled in this time period is, ${\text{Distance = }}\,{\text{Speed}} \times {\text{Time}}$
$ \Rightarrow {\text{Distance = }}\,70\,{\text{kmph}} \times {\text{0}}{\text{.71}}\,{\text{h}}$
\[ \Rightarrow {\text{Distance = }}\,49.7\,{\text{km}}\]
Now, the total distance covered by the train $ = 31.2 + 7.2 + 49.7$ kilometres $ = 88.1$ kilometres
Also, the total time taken $ = 0.52 + 0.24 + 0.71$ hours $ = 1.47$ hours
We know that ${\text{Average Speed = }}\dfrac{{{\text{Total Distance}}}}{{{\text{Total Time}}}}$.
So, we get, \[{\text{Average Speed = }}\dfrac{{88.1\,{\text{km}}}}{{{\text{1}}{\text{.47}}\,{\text{hr}}}}\]
\[ \Rightarrow {\text{Average Speed = }}59.93\] kilometres per hour
\[ \Rightarrow {\text{Average Speed }} \sim 60\] kilometres per hour
So, the average speed of the train is approximately $60$ kilometres per hour.
Hence, Proved.

Note:
The above-mentioned method can be remembered as a complete process for solving these types of questions. Be careful with the language while attending these types of questions, because there are many questions which may confuse you with the tricky and typical language. We must remember the formula relating the quantities distance, speed and time so as to solve the problem. These types of questions are easy to solve when you are writing an exam as it takes less time to solve when you are thorough with this concept and have practised ample amount of questions.