Question

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

Answer 1

Hint: We will first let the distance travelled by bus be $x$ km. Then, the distance travelled by aeroplane be $1900 - x$ km. Then, use the given condition ${\text{time = }}\dfrac{{{\text{distance}}}}{{{\text{speed}}}}$ to find the time taken by bus and aeroplane in the journey. Next, add the time and equate it to 5 and solve for the value of $x$ to find the distance travelled by bus.

Complete step-by-step answer:
We are given that the total distance covered by Vishal is 1900km.
Vishal travelled the sum distance by bus and some by aeroplane.
Let the distance travelled by bus is $x$ and then the distance travelled by aeroplane is $1900 - x$
We are also given that the speed of the bus is 60km/hr and the speed of the aeroplane is 700km/hr.
As it is known that ${\text{time = }}\dfrac{{{\text{distance}}}}{{{\text{speed}}}}$
Then the time taken by bus is $\dfrac{x}{{60}}$ and the time taken by aeroplane is $\dfrac{{1900 - x}}{{700}}$
We are also given that the total time taken by both bus and aeroplane is 5 hours.
This implies,
$\dfrac{x}{{60}} + \dfrac{{1900 - x}}{{700}} = 5$
Take the LCM to add LHS and then cross-multiply to form an equation.
$
  \dfrac{{35x + 3\left( {1900 - x} \right)}}{{2100}} = 5 \\
   \Rightarrow 32x + 5700 = 10500 \\
   \Rightarrow 32x = 4800 \\
$
On dividing the equation throughout by 32, we get,
$x = 150km$
Hence, the distance travelled by bus is 150km.

Note: Students should know the relation that time taken can be calculated by dividing distance from speed. Also, form the equation correctly and avoid calculation mistakes. Here, the distance is measured in kilometres.