train problem

Question

Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is ??

Comments

what is the distance between howrah to patna?

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no data given..

Answer 1

Ans- (4/3)

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      ->>>>  u                                                                      (v)<<<<-

 Howrah . --------------------------------   ----------------------Patna.
                                 x                                          y

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Let speed of train from Howrah to Patna = u

And speed of train from Patna to Howrah= v

Now let they meet at a distance x from Howrah and y from Patna after time t.

So t= (x/u ) = (y/ v) 

=> x/y = u/v  ----------------------------(1)

Now we are given that  y/u = 9 --------(A)

and x/v =16   ----------------(B)

Divide B by A.  We will get,     (x/y) * (u/v ) = 16/9

 From equation (1), replace x/y  by u/v,

  = >                                              (u/v)² = 16/9

  = >                                                u/v    = 4/3.

Comments

Great explanation dude :)

Answer 2

Let the distance be $x$.

Let the speed of first train be $a$ and that of second be $b$.

So, they meet after time $t$, where

$at + bt = x$

After this, first train reaches destination in 9 hours and second in 16 hours. So,

$bt/a = 9, at/b = 16 \\\implies a^2:b^2 = 16:9 \\ \implies a:b = 4:3. $

Answer 3

Let the speed of first train be x and that of second one be y.

After they meet first train travels distance=9x and second train travels distance=16y, Because distance=speed *time.

Now before they meet second train covers the distance 9x with velocity y. And first train covers the distance 16y with velocity x.

Since they start simultaneously so 9x/y = 16y/x.

Therefore x^2/y^2 = 16/9 or x/y = 4/3.