Question

A train 120 m long travelling at 45 km/hr overtakes another train travelling in the same direction at 36 km/ hr and passes it in 80 secs. Find the length of the train. (Please exaplain in detail)​

Answer 1

Answer:

Take the speed of the second train = x km/hr

They will have to cover a distance = sum of the lengths of the trains ( 150 + 100 = 250 m = 0.25 km )

Obtain their relative speed( x + 30 ) km/h & find out the time taken ( 10 sec = 10/3600 hr )

Equate it to 10s and solve for

( x + 30 ) =( 0.25/ 10 ) * 3600

x = 60 km/hr

Answer 2

Answer

Length of the train = 80 m

Given

A train 120 m long travelling at 45 km/hr overtakes another train travelling in the same direction at 36 km/ hr and passes it in 80 secs

To Find

Length of other train

Formula Applied

$\rm{\orange{\to\ Speed=\dfrac{Distance}{Time}\ \; \bigstar}}$

$\to\ \rm{\green{1\ Km/h=\dfrac{5}{18}\ m/s\ \; \bigstar}}$

Solution

Total distance , D = 120 + x m

Time , t = 80 s

Relative speed , S = 45 - 36 Km/h

$\rm \to\ S=9\ Km/h\\\\\rm \to\ S=9\times \dfrac{5}{18}\ m/s\\\\\rm \to\ S=\dfrac{5}{2}\ m/s$

Now , Apply formula ,

$\to\ \rm Speed=\dfrac{Distance}{Time}\\\\\to\ \rm S=\dfrac{D}{t}\\\\\to\ \rm \dfrac{5}{2}=\dfrac{120+x}{80}\\\\\to\ \rm 5\times 80=2(120+x)\\\\\to\ \rm 400=240+2x\\\\\to\ \rm 400-240=2x\\\\\to\ \rm 160=2x\\\\\to\ \rm 2x=160\\\\\to\ \rm x=80\ m\ \; \bigstar$

So , Length of the train = 80 m