Question

$\bold{Question}$


Ruhi travels 300 km to her home partially by train and partially by bus. She takes 4 hrs if she travels 60 km by train and remaining by bus. If she travel 100 km by train and remaining by bus, she takes 10 min longer, Find the speed of train and Bus.



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Answer 1

Step-by-step explanation:

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

so acc to ques. and using D=S/T

60/x+240/y=4........(1)

100/x+200/y=25/6.....(2)

now put 1/x=u and 1/y=v

60u+240v=4

15u+60v=1......(3)

100u+200v=25/6

u+2v=1/24......(4)

multiplying (4) by 15

15u+30v=5/8......(5)

subtracting (5) from (3)

30v=3/8

v=1/80    this implies y=1/v=80km/hr

put v=1/80 in (4)

u+2*1/80=1/24

u+1/40=1/24

u=1/24-1/40

u=2/120

u=1/60  this implies x=1/u=60 km/hr

hence speed of train=60km/hr and that of bus =80km/hr

Answer 2

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$\bf{https://brainly.in/question/37581179}$

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.

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