Question

Out of $1900km$, Vishal travelled some distance by bus and some by aeroplane. Bus travels with 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

Average speed of bus $=60km/h$.

Let the time taken in bus be $x$ hours.
Average speed of aeroplane $=700km/h$.
Let the time taken in aeroplane be $y$ hours.
Total distance covered $=1900km$

$\text{Distance}=\text{Speed}\times \text{Time}$

$\Rightarrow 60x+700y=1900$

$\Rightarrow 6x+70y=190$

$\Rightarrow 3x+35y=95$ ---(1)
It takes $5$ hours to complete the journey so,
$x+y=5$ ---(2)

$\Rightarrow x=5-y$

Substitute $x=5-y$ in $3x+35y=95$

$\Rightarrow 3(5-y)+35y=95$

$\Rightarrow 15-3y+35y=95$

$\Rightarrow 32y=95-15$

$\Rightarrow 32y=80$

$\Rightarrow y=\frac{80}{32}$

$\Rightarrow y=2.5$

Now, $x=5-y$

$\Rightarrow x=5-2.5=2.5$

Since, $\text{Distance}=\text{Speed}\times \text{Time}$

The distance travelled by Vishal by Bus $=60xkm$

$=60\times 2.5km$

$=150km$