Question

A train leaves New Delhi railway station at $ 9am $ and reaches Jaipur, which is at a distance of $ 260km $ at $ 12:45pm $ the train reaches Alwar at a distance $ 150km $ from Delhi at $ 11:30am $ and stop there for $ 15\min $ . What is the average speed of the train between Alwar and Jaipur?

Answer 1

Hint: Use the relation between speed, distance, and time. Find the distance between Alwar and Jaipur from the question and time taken by the train to reach from Alwar to Jaipur. We will get the required average speed.
 $ s = \dfrac{d}{t} $
Where $ s $ is the speed, $ d $ is the distance, $ t $ is the time.

Complete answer:
A train leaves New Delhi railway station at $ 9am $
Reaches Jaipur at $ 12:45pm $
Total time to reach Jaipur from New Delhi $ 3hours45\min $ that is $ 180 + 45\min = 225\min $
The same train reaches Alwar at $ 11:30am $
Total time to reach Alwar from New Delhi $ 2hours30\min $ that is $ 120 + 30\min = 150\min $
It is given that train stops of $ 15\min $ at Alwar.
Therefore train starts from Alwar to Jaipur after $ 165\min $
Total distance from Alwar to Jaipur will be the distance from New Delhi to Jaipur minus distance from New Delhi to Alwar $ 260km - 150km = 110km $
Total time is taken by the train to reach from Alwar to Jaipur $ 225\min - 165\min = 60\min $
We know $ 60\min = 1hour $
So $ s = \dfrac{d}{t} $
Where $ s $ is the speed, $ d $ is the distance, $ t $ is the time
 $ \Rightarrow s = \dfrac{{110}}{{1(hour)}} $
Hence, the average speed of the train between Alwar and Jaipur is $ 110\dfrac{{km}}{{hour}} $ .

Note:
The units of all the physical quantities should be in the same system. For example: if the distance is given in kilometres and time is given in hours, then speed will be calculated in kilometres per hour initially. Then, we convert the unit of speed using the conversion rate. To convert from $ \dfrac{{km}}{{hr}} $ to $ \dfrac{m}{\operatorname{s} } $ , we multiply by $ \dfrac{5}{{18}} $ .