Question

Roohi travels 300 km to her home partly by train and partly by bus . she takes 4 hours if she travels 60km by train and remaining by bus. if she travels 100 km by train and remaining by bus, she takes 10minutes longer. find the speed of the train and the bus

Answer 1

Let the speed of train be x km/hr and the speed of bus be y km/hr.
Case I. When she travels 60 km by train and the rest by bus.
Time taken by Roohi to travel 60 km by train = 60/x hours
Time taken by Roohi to travel (300 - 60) = 240 km by bus = 240/y hours.
Therefore, Total time taken by Roohi to cover 300 km = 60/x + 240/y
Given, total time = 4 hours.
Therefore, 60/x + 240/y = 4
Or, 15/x + 60/y = 1

Case II. When she travels 100 km by train and the rest by bus.
Time taken by Roohi to travel 100 km by train = 100/x hours
Time taken by Roohi to travel (300 - 100) = 200 km by bus = 200/y hours.
Since, Total time of the journey is 4 hours 10 minutes,
Therefore, 100/x + 200/y = 4 10/60 = 25/6
Or, 4/x + 8/y = 1/6
Thus, we obtain the following system of equations :
15/x + 60/y = 1, 4/x + 8/y = 1/6
By solving these two equations, we obtain x = 60 and y = 80.
Therefore, Speed of train = 60 km/hr, Speed of bus = 80 km/hr.

Answer 2

$\huge\bf\purple{\mid{\fbox{\underline{\underline{Answer}}}}\mid}$

Let the speed of train and bus be u km/h and v km/h respectively.

According to the question,

$\frac{60}{u} + \frac{240}{v} = 4$....(i)

$\frac{100}{u} + \frac{200}{v} = 4 + \frac{10}{60} = \frac{25}{6}$....(ii)

Let $\frac{1}{u} = p\: and \frac{1}{v} = q$

The given equations reduce to:

60p + 240q = 4 ....(iii)

100p + 200q = $\frac{25}{6}$

600p + 1200q = 25....(iv)

Multiplying equation (iii) by 10, we obtain:

600p + 2400q = 40....(v)

Subtracting equation (iv) from equation (v), we obtain:

1200q = 15

q = $\frac{15}{1200} = \frac{1}{80}$

Substituting the value of q in equation (iii), we obtain:

60p + 3 = 4

60p = 1

p = $\frac{1}{60}$

:. p = $\frac{1}{u} = \frac{1}{60}$, q = $\frac{1}{v} = \frac{1}{80}$

u = 60 km/h , v = 80 km/h

Thus, the speed of train and the speed of bus are 60 km/h and 80 km/h respectively.

HOPE IT HELPS

PLEASE MARK ME BRAINLIEST ☺️

https://brainly.in/question/37581179