Cognizant Time Speed and Distance Quiz-1

Since the train and man are moving in opposite directions,

The relative speed = 60-(-6) kph = 60 + 6 = 66 kph

66 km/h in m/s = 66*5/18 = 55/3 m/s

Total distance to be covered = 110 m (length of the train)

So, time = distance/speed = 110 divided by 55/3 which equals 6 s.

speed of first train=\frac{x}{18}m/sec

speed of Second train=\frac{x}{12}m/sec

When both trains cross each other, time taken

\frac{2x}{\frac{x}{18}+\frac{x}{12}}

\frac{2x}{\frac{2x+3x}{36}}

\frac{72}{5}=14.4 sec

(x+100)/25 = x/15

=> 15(x + 100) = 25x

=> 15x + 1500 = 25x

=> 1500 = 10x

=> x = 150 m.

Given speed = 63 km/hr = 63×5/18=17.5 m/s

Let the length of the bridge = x mts

Given time taken to cover the distance of (170 + x)mts is 30 sec.

We know speed = distance/time

⇒17.5=170+x/30

--> x = 355 mts.

Let the speed of the current be x km/hr
Thus upward speed =(4.5+x) km/hr
and downward speed =(4.5−x) km/hr

Let distance travelled be y, then
y
(4.5−x)
=
2y
(4.5+x)

⇒ x= 1.5 km/hr

Let the total distance covered be S km.
Total time taken=
S/(2×40)+S/(2×60)=5S/240hr
Average speed =S*240/5S

= 48 km/hr

Let the speed of the cyclist be x km/h and wind be y km/h
1/(x+y)=3/60
X+y=20..........i

And
1/(x-y)=4/60
x-y==15.........ii
On solving both the equations we get:
x=35/2
,y=5/2
Now, time taken by cyclist without wind: (2/35)*60=24/7 min

Let the speed of the stream be x km/hr. Then,

Speed downstream = (15 + x) km/hr,

Speed upstream = (15 - x) km/hr.

30/(15 + x) + 30/ (15 - x) = 4 1/2
900/(225 - x²) = 9/2
9x² = 225

x² = 25

x = 5 km/hr.

Let the speed of goods train be x km/hr.
Then, (50+x)×(5/18)=187.5/9

⇒ x= 25 km/hr

Speed of boat downstream

= Distance coveredTime taken=30/2 = 15 km/h

Now, speed of boat upstream

= Distance coveredTime taken=30/6 = 5 km/h

Now, speed of boat

= (Speed downstream+Speed upstream)/2

= (15+5)/2=20/2 = 10 km/h