Question

Out of 1900 km, Vishal travelled some distance by bus and some by airplane. The bus travels with an average speed of 60 km / hr. and the average speed of the airplane is 700 km/hr. It takes 5 hours to complete the journey. Find the distance, Vishal travelled by bus in km.

Answer 1

Hint: We will equate the time by adding the time through both the journeys, airplane and bus and then put them equal to 5 to get the required answer.

Complete step-by-step answer:
We know that we have a formula of distance related to speed and time, given by the following expression:-
$ \Rightarrow Dis\tan ce = Speed \times Time$
Rearranging terms to find time from it, we will then get:-
$ \Rightarrow Time = \dfrac{{Dis\tan ce}}{{Speed}}$
Let us assume that Vishal covered x km by bus and (1900 – x) km by airplane because in total, he covered 1900 km.
Now, since the average speed of a bus is 60 km / hr and the speed of an airplane is 700 km / hr.
So, using the formula of time, we will get:-
Time spent by Vishal in bus = $\dfrac{x}{{60}}$ hours and the time spent b Vishal is airplane = $\dfrac{{1900 - x}}{{700}}$ hours.
Now, in total he spent 5 hours in travelling, therefore, we get:-
$ \Rightarrow \dfrac{x}{{60}} + \dfrac{{1900 - x}}{{700}} = 5$
Taking the L. C. M. of 60 and 700, we will get: 2100 and thus we can write the above expression in the following representation:-
$ \Rightarrow \dfrac{{35x + 3\left( {1900 - x} \right)}}{{2100}} = 5$
Taking the 2100 from division in the left hand side to multiplication in the right hand side to obtain:-
$ \Rightarrow 35x + 3\left( {1900 - x} \right) = 5 \times 2100$
Opening up the bracket in the left side and doing the calculations in the right hand to obtain:-
$ \Rightarrow 35x + 5700 - 3x = 10500$
Simplifying the left hand side a bit by clubbing the terms with x together, we will then obtain:-
$ \Rightarrow 32x + 5700 = 10500$
Taking 5700 from addition in the left hand side to subtraction in the right hand side to obtain:-
$ \Rightarrow 32x = 10500 - 5700$
Simplifying the calculation on the right hand side of the above expression to obtain:-
$ \Rightarrow 32x = 4800$
Taking the 32 from multiplication in left hand side to division in the right hand side to obtain:-
$ \Rightarrow x = \dfrac{{4800}}{{32}}$
Simplifying the calculation, we will then obtain:-
$ \Rightarrow x = 150$
Hence, he covers 150 km by bus and thus 1900 – 150 = 1750 km by airplane.

Hence, the answer is 150 km.

Note:
The students must note that we compared time on both sides in the equation we formed in the beginning, you may also compare and equate the speed as well using the same time, speed and distance formula and would have got the same answer.
The students must note that looking at the units of everything is really necessary, since it is possible that you are given speed in meter / hour or meters / minute or anything of that sorts, then you will be required to convert them in km / hr to proceed further to obtain the answer.