Word Problem 1 ( Trains running in the same direction )

Problem 1 : There are two trains namely T1 and T2, with lengths of 65 m and 55 m respectively, and are running in the same direction with speeds of 20 km/hr and 47 km/hr respectively. The faster train will cross totally the slower one in how many seconds ?


Length of Train T1;

L1 = 65m

Length of Train T2;

L2 = 55m

Speed of train T1;

v1=20 \frac {km}{h}

Speed of train T2;

v2=47 \frac {km}{h}

As Train T2 is moving faster than Train T1 so, the net speed by which Train T2 will cross Train T1 is given by;

v2,net=47 \frac {km}{h} -20 \frac {km}{h}

v2,net=27 \frac {km}{h}

Because there are 1000 meters in ikm and 3600 seconds in 1 hour, so;

v2 , net = 27\times \frac{1000m}{3600sec}

\Rightarrow v2, net=7.5\frac{m}{sec}

Train T2 while crossing Train T1 with net speed of 7.5 m/sec  will cover distance equal to sum of lengths of both trains;

so we use formula;


t= \frac{S}{v}

Put  distance, S= L1+L2=65+55=120m

and for Train T2 net speed;

v= 7.5 \frac{m}{s}

We get,

\Rightarrow t= \frac{120}{7.5}

\Rightarrow t= 16 sec

So. Train T2 will completely cross Train T1 in 16 seconds.

(basic mathematics for general public)




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