Question

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

Answer 1

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

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ANSWER

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

So according to question and using Time=

Speed

Distance

Total distance =300 km

Roohi travels 60 km by train and 300−60=240 by bus in 4 minute,

x

60

+

y

240

=4

and 100 km by train, 300−100=200 by bus, and takes 10 minutes more,

x

100

+

y

200

=4+

60

10

⇒

x

100

+

y

200

=

6

25

Now, let

x

1

=u and

y

1

=v

then 60u+240v=4.............eq1

100u+200v=

6

25

..............eq2

multiply eq1 by 5 and eq2 by 6 we get

300u+1200v=20..........eq3

600u+1200v=25...........eq4

Subtracting eq3 qnd eq4 we get

−300u=−5

u=

300

5

=

60

1

Putting the value of u in eq1 we get

60×

60

1

+240v=4

240v=3

v=

240

3

=

80

1

Now

x

1

=u=

60

1

∴x=60

and

y

1

=v=

80

1

∴y=80

Hence the speed of the train is 60 km/hr and the speed of the bus is 80 km/hr.

Step-by-step explanation:

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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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