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 the remaining 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 separtely.

Answer 1

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

so according to question. 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 means x=1/u=60 km/hr

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

Answer 2

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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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