Question

A goods train and a passenger train are running on the parallel tracks in the same direction. the driver of the goods train observes that the passenger train coming from behind, overtakes and crosses his train completely in 1 min whereas a passenger on the passenger train marks that he crosses the goods train in 1/3 min. if the speeds of the trains is in the ratio of 1 : 2, then find the ratio of their lengths

Answer 1

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Answer 2

Answer:

the ratio of the length of the trains = 1:2

Solution:

The ratio of the speed of the trains are 1:2

Let us assume the speeds are s and 2s and also assume that the length of the trains are A and B.

The driver of goods train observes that the passenger crosses his train in 1 min = 60 sec.

So,  $\frac{A+B}{2 s-s}= 60$ ------------- (i)

The passenger train observes that he passed good train in $\frac{1}{3} \min =\frac{60}{3}=20 \mathrm{sec}$

So, $\frac{A}{2 s-s}=20$ ------------ (ii)

Now dividing (i) by (ii)

$\frac{A+B}{A}=\frac{60}{20}$

$1+\frac{B}{A}=3$

$\frac{B}{A}=2$

$\frac{A}{B}=\frac{1}{2}$

So the ratio of the length = 1:2