Question

Mansi travels 300 kms to her native partly by train and partly by bus. She takes

4 hours, if she travels 60 kms by train and the remaining by bus. lf she travels 1 00 kms

by train and the remaining by bus, she takes 10 minutes longer. Find the average

speed of the train and the bus separately.

​

Answer 1

Step-by-step explanation:

So according to question and using

Time = \frac{Distance}{speed}Time=

speed

Distance

Total distance =300 km

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

\frac{60}{x} + \frac{240}{y} = 4

x

60

+

y

240

=4

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

\frac{100}{x} + \frac{200}{y} = 4 + \frac{1}{6} = \frac{24 + 1 }{6} = \frac{25}{6}

x

100

+

y

200

=4+

6

1

=

6

24+1

=

6

25

Now, let

\frac{1}{x} = a \:

x

1

=a

and

\frac{1}{y} = b

y

1

=b

then 60a+240b=4.............(1)

100a+200b=25/6----(2)

multiply (1) by 5 and (2) by 6 we get

300a+1200b=20..........(3)

600a+1200b=25...........(4)

Subtracting (3) and (4) we get

−300a=−5

a = \frac{1}{60}a=

60

1

Putting the value of a in (1) we get

60 \times \frac{1}{60} + 240b = 460×

60

1

+240b=4

\begin{gathered}240b = 3 \\ b = \frac{1}{80} \end{gathered}

240b=3

b=

80

1

Now ,

\begin{gathered} \frac{1}{x} = a \\ a = 60 km/h\end{gathered}

x

1

=a

a=60km/h

\begin{gathered} \frac{1}{y} = b \\ b = 80 km/h\end{gathered}

y

1

=b

b=80km/h

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

Answer 2

$\huge\bf\purple{\mid{\fbox{\underline{\underline{Answer}}}}\mid}$

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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