Question

Mansi travels 300 kms to her native partly by train and partly by bus. She takes
4 hours, if she travels 60 kms by train and the remaining by bus. If she travels 100 kms by train and the remaining by bus, she takes 10 minutes longer. Find the average speed of the train and the bus separately. step by step

Answer 1

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

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

$\frac{60}{x} + \frac{240}{y} = 4 </p><p>$

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

$\frac{1}{x} = u </p><p>$

and

$\frac{1}{y} = v </p><p>$

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 and 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

$</p><p>\frac{1}{x} = u = \frac{1}{60} </p><p>$

∴x=60

and

$</p><p>\frac{1}{y} = v = \frac{1}{80} </p><p>$

∴y=80

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

Answer 2

Answer:

in this case ,

y = 80

hope this will helps u......be happy.......