Question

mun alone to
(ii) Roohi travels 300 km
hours if she travels 60 kr
by train and the remaining by by
by train and partly by bus. She takes 4
els 300 km to her home partly by train and partly by bus
and the remaining by bus. If she travels 100 km
nining by bus, she takes 10 minutes longer. Find the speed of
the train and the bus separately.​

Answer 1

speed of the train = xkm/hr

speed of bus = ykm/ hr

60/x + 240/y = 4

100/x + 200/y = 25/6

1/x =p

1/y = q

by using elimination method we get

6000p + 24000q = 400

6000p + 12000q = 250

________________________

12000q = 150

q = 1/180

60p+ 240× 1/80 = 4

p = 1/60

x = 60km/hr

y = 80 km/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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