Question

A train travelled $418\,km$ at an average speed of $95\,km/h$. How long did the journey take?

Answer 1

Hint: The average speed of a body in a certain time interval is the total distance covered by the body in that time interval divided by the time interval so if a particle covers a certain distance \[s\] in a time\[t\] then the average velocity is given by \[{V_{av}} = \dfrac{s}{t}\]. We have distance and average speed is given and we have to calculate the time interval taken by the train to cover the given distance.

Complete step by step answer:
Here we have given average speed, and the total distance covered by the train in some interval of time and we have to calculate that time interval.Now as we have given that,
Distance travelled the train, \[s = 418\,km\]
Average speed of the train, \[{V_{av}} = 95\,km/h\]
Time travelled by the train to cover that distance, \[t = ?\]
From the formula of average speed we have, \[{V_{av}} = \dfrac{s}{t}\]
By changing the sides of average velocity and time in order to obtain the time we have
 \[t = \dfrac{s}{{{V_{av}}}}\]
Substituting the values given, we get;
\[t = \dfrac{{418}}{{95}}\]
On doing simple division we get
\[ \therefore t = {\text{4}}{\text{.4}}\,h\]

Hence the train will take 4.4 hr to travel 418 km at an average speed of 95 km/h.

Note:The question might be differ by changing the magnitudes of the quantity. Also there might be change in the unit of measurement like there could be m/s instead of km/h. One should also know the difference between average speed and the average velocity in order to solve similar questions in linear line. Average velocity is the total displacement divided by the total time taken.