tricky math question?

Question

mike was walking through a railway train tunnel when he suddenly heard a train approaching. looking at the markers inside the tunnel, he saw that he was 2/5 the distance from one end of the tunnel and 3/5 the distance from teh other end of the tunnel.

if mike runs as fast as he can towards either end, he will escape from the tunnel just as the train reaches him.

if the train is moving 60km/h, how fast is mike running?

thanks for the answers!

Answer 1

Let the length of the tunnel be 5d (meters).

Now, you said if Mike runs to either end at some speed, he'll escape as the train reaches him. But the train only comes in from one end. So, the shorter distance, 2d must be the distance he covers running towards the train. 3d is the distance he covers if he tries to run away from the train.

Speed of train = 60km/h = (50/3) m/s
Let Mike's speed both ways be x m/s

Let the train be distance D from the end of the tunnel which is closer to Mike. They both reach the end at the same time.

Time = Distance/Speed.

Using the above equation,
2d/x = D/60
120d = Dx ..... (1)

Now assume Mike runs towards the far end of the tunnel, 3d distance from him. Again, the train catches up just as he escapes. So, time taken is equal again. Now the train has to cover D as well as 5d, the length of the tunnel,

3d/x = (D + 5d)/60
180d = Dx + 5dx
180d = 120d + 5dx [From (1)]
60d = 5dx
x = 60d/5d
x = 12

Speed of Mike = 12m/s = (216/5)km/h = 43.2 km/h

Answer 2

let mike's speed = v, and
tunnel be x km long

2/5 has to be the end of the tunnel that the train is coming through. if not, mike would've just taken the shorter route that would also allow him longer time for the train to reach him.

mike would escape either route, right?
and the train'd reach him that same moment in both accounts. because mike is running at constant rate, the time he'd take running the longer escape route is (3/5 divide by 2/5) = 1.5 times the span of running the short-cut.

difference of time
= (3x/5)/v - (2x/5)/v
= x/5v

and in that difference of time, x/5v, the train could cover the distance of whole tunnel.
train's moving at the same time, with speed 60 and distance x.

x/60 = x/5v
5v = 60
v = 12 km/h

answer = 12 km/h

Answer 3

you first of all should write equation for train to understand how much long does it take that train pass the tunnel Train equation : (you should choose point as or gin: i suppose where train is ) train have a constant speed so we use this equation x=v t+x. x.=0 (initial position)
5=60*(10/36) t+0 (change the unit to SI from km/h to m/s)
t=33.3 second time that take train pass the tunnel
Mike does not have constant speed so he have acceleration because he start running & we know that he would go out of the tunnel in 3.33 second
Mike equation : x=1/2at^2+v.t+x.
6=1/2a(3.33)^2+(0)(3.33)+3.5 ( i didn't understand from the question that Mike escape the tunnel from which end the that 3.5 long or the end 2.5 i suppose he escape from the end that it long 2.5 if it is wrong you change 3.5 with 2.5 )
a=0.45 m/s^2
we know V=a t + V. (t=3.33 second)
V=0.45*(3.33)+0
V=1.5 m/s V=5.4 km/s
I thanks GOD that help me can help you
I hope as an iranian people nice time for you.

Answer 4

In other words, time for mike to run 3/5 distance = time for the train to cover whole (5/5 or 1) distance.

since distance = speed * time, then time = distance / speed.
We apply it to both mike and train, gives

(3/5)/mike speed = 1 / 60
mike speed = (3/5)*60
= 36 km/h

Answer 5

Not fast enough to live?

Answer 6

He's dead