Question

ROOHI TRAVELS 300 KM TO HER HOME PARTLY BY TRAIN AND PARTLY BY BUS SHE TAKES FOUR HOURS IF SHE TRAVELS 60KM BY TRAIN AND THE REAMAINING BY BUS IF SHE TRAVELS 100KM BY TRAIN AND THE REMAINING BY BUS SHE TAKES 10 MINUTES LONGER FIND THE SPEED OF THE TRAIN AND THE BUS SEPARATELY

Answer 1

pls see d attachment 1st and the speed of the bus is 80km

Answer 2

Let the speed of the train be x km/hr and the speed of the bus is y km/hr.

So according to question and using Time= Speed/

Distance

Total distance =300 km

Roohi travels 60 km by train and 300−60=240 by bus in 4 minute,

$\frac{60}{x} + \frac{240}{y} = 4$

and 100 km by train, 300−100=200 by bus, and takes 10 minutes more,

$⇒ \frac{100}{x} + \frac{200}{y} = 4 + \frac{10}{60}$

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

Now, let

$\frac{1}{x} = u$

and

$\frac{1}{y} = v$

then 60u+240v=4.............eq1

100u+200v= 6/25 ..............eq2

multiply eq1 by 5 and eq2 by 6 we get

300u+1200v=20..........eq3

600u+1200v=25...........eq4

Subtracting eq3 qnd eq4 we get

$- 300u = - 5$

$u = \frac{5}{300} = \frac{1}{60}$

Putting the value of u in eq1 we get

$60 \times \frac{1}{60} + 240v = 4$

$240v = 3$

$v = \frac{3}{240} = \frac{1}{80}$

Now

$\frac{1}{x} = u = \frac{1}{60}$

∴x=60

and

$\frac{1}{y} = v = \frac{1}{80}$

∴y=80

Hence the speed of the train is 60 km/hr and the speed of the bus is 80 km/hr.