Question

A bus covers 128KM in 2 hours and a train covers 240KM in 3 hours. Find their speeds.

Answer 1

Hint:
We will use the formula for the speed of an object when the distance covered and the time taken is given. The speed of an object can be found by dividing the distance it has covered by the time it took to cover that distance. We will substitute the values of distance and time in the formula and find the speed.

Formulas used: We will use the formula \[{\rm{Speed}} = \dfrac{{{\rm{Distance}}}}{{{\rm{Time}}}}\] to solve the question.

Complete step by step solution:
We know that the bus covered 128 Km in 2 hours.
Substituting 128 for the distance and 2 for the time in the formula for speed, \[{\rm{Speed}} = \dfrac{{{\rm{Distance}}}}{{{\rm{Time}}}}\], we get
\[\begin{array}{l}{\rm{Speed}} = \dfrac{{128{\rm{ km}}}}{{2{\rm{ hr}}}}\\{\rm{Speed}} = 64{\rm{ km/hr}}\end{array}\]
We know that the train covered 240 Km in 3 hours.
Substituting 240 for the distance and 3 for the time in the formula for speed , \[{\rm{Speed}} = \dfrac{{{\rm{Distance}}}}{{{\rm{Time}}}}\], we get
\[\begin{array}{l}{\rm{Speed}} = \dfrac{{{\rm{240km}}}}{{{\rm{3hr}}}}\\{\rm{Speed}} = 80{\rm{km/hr}}\end{array}\]

$\therefore $ The speed of the bus is \[64{\rm{km/hr}}\] and the speed of the train is \[80{\rm{km/hr}}\].

Note:
The S.I. unit of speed is metre per second (\[{\rm{m/s}}\]). Kilometre per hour (\[{\rm{km/hr}}\]) is also an accepted unit to represent the speed of an object. If we encounter a problem where the distance covered is given in kilometers and the time is given in minutes or seconds we must remember to either convert the distance into metres or the time into hours. Similarly, if we encounter a problem where the distance is given in metres and the time in hours, we must remember to either convert the time into seconds or the distance into kilometres. This will help us in getting the correct unit for the speed. Let us enlist the formulas for the conversion of units below:
\[\begin{array}{c}1{\rm{ Km}} = 1000{\rm{ m}}\\{\rm{1 m}} = 0.001{\rm{ Km}}\\1{\rm{ minute}} = 60{\rm{ seconds}}\\{\rm{1 hour}} = 60{\rm{ minutes}}\\{\rm{1 hour}} = 3600{\rm{ seconds}}\end{array}\]