Question

Two trains start simultaneously from two stations 300 km apart and move towards each other. The speed of one train is more than the other by 20 km/hr. If the distance between the trains after two hours is 20 km, find the speeds of the trains.​

Answer 1

$\rm\orange{Given:}$

• The distance between two stations=$\rm{300\:km}$

$\rm\blue{To\:find:}$

• The speeds of the trains.

$\rm\red{Solution:}$

Let us take the speed of a first train be $\rm{x\:km/h}$

∴ speed of the other train $\rm{=(x+20)km/hr }$

•Distance travel by the first train in $\rm{1\:hr=x\:km}$

•Distance travelled by first train in $\rm{2\:hrs=(2x)\:km}$

•Distance travelled by other train in $\rm{1\:hrs=(x+20)\:km}$

•Distance travelled by other train in $\rm{2\:hrs=2(x+20)=(2x+40)\:km}$

The distance between two stations is $\rm{300\:km}$

According to given situation,

Distance travelled by first train $\rm{+}$ Distance travelled by other train $\rm{+20=300}$

$\rm\leadsto{2x+(2x+40)+20=300}$

$\rm\leadsto{2x+2x+40+20=300}$

$\rm\leadsto{4x+60=300}$

$\rm\leadsto{4x=300-60}$

$\rm\leadsto{4x=240}$

$\rm\leadsto{x=}\dfrac{240}{4}$

$\rm\leadsto{x=60}$

Therefore,the speed of first train=$\rm{60\:km/h }$

Speed of the other train $\rm{ =(60+20)=80\:km/hr }$

Let's verify our Answer.

$\rm\green{Verification:}$

•Distance travelled by first train in $\rm{2\:hrs=(2×60)km=120km }$

•Distance travelled by other train in $\rm{2\:hrs=(2×80)\:km=160\:km}$

•Distance between two trains after $\rm{2\:hrs=300-(120+160)=300-280=20\:km}$

Hence, the speeds of the train are $\rm{ 60km/hr\:\:and\:\: 80km/hr. }$