Question

A train approaches a 800m long tunnel AB. Inside the tunnel there is a rabbit. When the train whistles the rabbit runs. If the rabbit moves to the entrance of the tunnel A, the train catches the rabbit exactly at the entrance. If the rabbit moves to the exit B, the train catches the cat exactly at the exit. If the speed of the train is four times the speed of the rabbit what is the distance of the point at which train whistles from the entrance of the tunnel?

Answer 1

2400 m is the distance from the train whistles to the entrance of the tunnel.

Step-by-step explanation:

Given:

          Speed of train '$s_{t}$' = 4 x speed of rabbit '$s_{r}$'

          Tunnel is 800 m long.

          The train catches the rabbit at the entrance and the exit after the train whistles.

               As we know speed s = $\frac{d}{t}$

                           time t = $\frac{d}{s}$                  .........    (1)

     Condition - when the train hit the rabbit at the exit.

                    Let distance of rabbit to exit is 'x' and the distance from train to exit tunnel is 'y'.

               

 So, from equation (1),

                     

                     Both have taken same time to reach exit of tunnel.

                        ⇒ $\frac{y}{s_{t}} = \frac{x}{s_{r}}$

                        ⇒  x = $\frac{y}{4}$

Now,

           Condition - when the train hit the rabbit at entrance of tunnel.

                                           ⇒   $\frac{y-800}{s_{t} } = \frac{800 - x}{s_{r} }$

                                           ⇒ $\frac{y-800}{4} = \frac{800 - x}{1}$  

After solving this,

                                         ⇒  x + y  = 4000 m

Put,                            

    ⇒  x = $\frac{y}{4}$

Now, Now from both the equations,

                                   ⇒  $\frac{5y}{4} = 4000$

So,                              ⇒ y = 3200

       

             Now, the distance from train whistles to the rabbit is

                                        = y - 800

                                        = 3200 - 800

                                    = 2400 m                      

Answer 2

Answer:

1200m

Step-by-step explanation:

Train_______ππππRabbit ππππππππ

|---Dt------|--------------800m---------|

Dt |--D---|-------800-D-------|

Distance from train to tunnel entrance= D2

Distance from train to tunnel exit = Dt + 800m

Distance from rabbit to tunnel entrance= D

Distance from rabbit to tunnel exit = 800m - D

Speeds = 4s (Train) and s for(Rabbit )

Since time (T1) is same for rabbit and train to tunnel entrance => D/s=Dt/4s

Therefore, Dt=4D.

and time (T2) is same for them to reach the exit,

=> (800-D)/s = (800+Dt)/4s

=> (800-D)/1 = (800+4D)/4

=> 4*(800-D) = (800+4D)

=> 3200-4D=800+4D

=>2400=8D

=>D=300

=>Dt=4*300=1200m (distance from train to π tunnel)

Answer is 1200m .

What the previous person did wrong was 4000=4x+y ...(he had to multiply 4 with both 400 and x...and therefore got the answer wrong, but the concept was same ofcourse :)