Quiz 1

Explanation:
Relative speed =280/9 m / sec
=\frac {280}{9}\times \frac{18}{5}
=112kmph
Speed of goods train = (112 - 50) kmph = 62 kmph.

Explanation:
Distance = 110 m

Relative speed = 60 + 6 = 66 kmph (Since both the train and the man are in moving in opposite direction)

66\times \frac{5}{18}=\frac{55}{3} m/sec

Time taken to pass the man = 110\times \frac{3}{55} = 6 s

Explanation:
Speed of the train relative to man = (\frac{125}{10}) m/sec = \frac{25}{2} m/sec.
[\frac{25}{2} \times \frac{18}{5} ] km/hr = 45 km/hr.
Let the speed of the train be 'S' km/hr.
Then, relative speed = (S - 5) km/hr.
S - 5 = 45 => S = 50 km/hr.

Explanation:
Speed of the Train K is given by s = d/t = \frac {240}{20}= 12 m/s
Distance covered by Train K in 50 seconds = 12 x 50 = 600 mts.
But it crosses Train L in 50 seconds
Therefore, the length of the Train L is = 600 - 240 = 360 mts.

Explanation:
1h ----- 5 kms
? ------ 60 kms

Time = 12 hrs

Relative Speed = 16 + 21 = 37 kmph

T = 12 hrs

D = S x T = 37 x 12 = 444 kms.

Explanation:
Next train comes at 17:00 hrs.
So, last train will be = 17:00hrs - 2:30hrs
= 14:30hrs
Announcement made after 37 min of the last train.
S0, 14:30hrs + 00:37 min
= 15:07 hrs.

Explanation:
Let the speed of the faster train be 'X' kmph,
Then their relative speed= X - 48 kmph
To cross slower train by faster train,
Distance need to be cover = (400 + 600)m = 1 km. and
Time required = 180 sec = \frac{180}{3600}hr = \frac{1}{20} hr.
Time = Distance/Speed
\frac{1}{20} = \frac{1}{x-48}
x = 68 kmph

Explanation:
Given speed of the first train = 60 km/hr = 60 x 5/18 = 50/3 m/s

Let the speed of the second train = x m/s

Then, the difference in the speed is given by
\frac{50}{3}-x=\frac{120}{18}
x=10 m/sec
x=10\times \frac{18}{5}
x=36kmph

Explanation:
Speed=78\times \frac{5}{18} m/sec
=\frac{65}{3} m/sec

Time=1minute=60 seconds
Let the length of the tunnel be x metres.
Then, [\frac{800+x}{60}]= \frac{65}{3}
3(800 + x) = 3900
x=500m

Explanation:

Length of the train =150 m
Speed of the man = 2 km/hr

Relative speed = \frac{150}{3} = 50m/s

= 50 \times \frac{18}{5} = 180km/hr [/latex]

Relative speed = Speed of train - Speed of the man (as both are moving in the same direction).

Speed of the train = Relative speed + Speed of the man = 180 + 2  = 182 km/hr