Relative Speed-RRB

Time, Speed and Distance-RRB Relative Speed-RRB

Relative Speed

If two trains are moving in opposite directions with speed limits of X km/hr and Y km/hr respectively, then (X + Y) is the relative speed.

If two trains are moving in same direction with speed limits of X km/hr and Y km/hr respectively, then (X – Y) is the relative speed.

The time taken by the trains in passing each other when moving in opposite direction. = $\frac{(L1+L2)}{(x+y)}$ hours., L1 and L2 are lengths of two trains.

The time taken by the trains in passing each other, when moving in same direction = $\frac{(L1+L2)}{(x-y)}$ hours., L1 and L2 are lengths of two trains.

Question 1:

Two trains 100 m and 80 m length each are running in same direction. The first runs at the rate of 60 m/s and the second at the rate of 51 m/s. How long will they take to cross each other ?

Solution

The relative speed = 60-51 =9 m/s.( since trains are running in the same direction).Hence the time taken by trains in crossing each other is $\frac{100+80}{9}$ = 20 second.

Question 2:

Two trains 100 m and 80 m length each are running in opposite direction. The first runs at the rate of 10 m/s and the second at the rate of 8 m/s. How long will they take to cross each other ?

Solution

The relative speed here is 10 + 8 = 18 m/s. (since trains are running in the same direction). Hence the time taken by trains in crossing each other is $\frac{100+80}{18}$ = 10 second.

Question 3:

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

Solution:

Speed of the train relative to man = (125/10) m/sec

= (25/2) m/sec

= (25/2 x 18/5) km/hr

= 45 km/hr

Let the speed of the train be x km/hr. Then, relative speed = (x – 5) km/hr.

x – 5 = 45

=> x = 50 km/hr.

Question 4:

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

Solution:

Let the speeds of the two trains be x m/sec and y m/sec respectively.

Then, length of the first train = 27x metres,

and length of the second train = 17y metres.

27x + 17y/ x + y = 23

=> 27x + 17y = 23x + 23y

=> 4x = 6y

=> x/y = 3/2

Question 5:

A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

Solution:

Speed = (54 x 5/18) m/sec = 15 m/sec

Length of the train = (15 x 20)m = 300 m.

Let the length of the platform be x metres.

Then, x + 300/ 36 = 15

=> x + 300 = 540

=> x = 240 m.

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