Question

Shweta travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately. [4 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

Let the speed of the train be $tkm/hr$ and speed of the bus be $bkm/hr$

Then,

Time taken by Shweta to travel by train is

$=\frac{60}{t}$ [$\because time=\frac{dist}{speed}$]

Time taken by Shweta to travel by bus is

$=\frac{240}{b}$ [$\because$ Remainimg distance = 300 km - 60 km]

Total time taken is 4 hrs

$\Rightarrow \frac{60}{t}+\frac{240}{b}=4\dots \dots \left(i\right)$

Similarly

$\frac{100}{t}+\frac{200}{b}=\frac{25}{6}\dots \dots \left(ii\right)$

[$\because 4hr10min=4\frac{10}{60}=\frac{25}{6}$]

Let $\frac{1}{t}=xand\frac{1}{b}=y$

Then (i) reduces to,

$60x+240y=\mathrm{4......}\left(iii\right)$

(ii) reduces to ,

$100x+200y=\frac{25}{6}$

$\Rightarrow 4x+8y=\frac{1}{6}......\left(iv\right)$

$15\times \left(iv\right)\Rightarrow$

$60x+120y=\frac{5}{2}.....\left(v\right)$

Subtracting (v) from (iii) we get,

$60x+240y-60x-120y=4-\frac{5}{2}$

$120y=\frac{3}{2}\Rightarrow y=\frac{1}{80}$

$\Rightarrow \frac{1}{b}=\frac{1}{80}$

$\Rightarrow b=80$

Substituting value of y in (iii)

$60x+240\left(\frac{1}{80}\right)=4\Rightarrow x=\frac{1}{60}$

$\Rightarrow \frac{1}{t}=\frac{1}{60}$

$\Rightarrow t=60$

$\therefore t=60,b=80$

$\therefore$ The speed of the train is $60km/hr$ and speed of the bus is $80km/hr$.