Question

roohi travels 300km to her home partly by train and partly by bus.she takes 4 hrs if she travels 60kmby train and the remaining by bus.if she travels 100km by bus,she takes 10mins longer.find the speed of the train and bus seperately.

Answer 1

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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