Question

the distance between the two station is 425 km two train start simultaneously from the stations on parallel tracks to cross each other the speed of one of them is greater than that of the other by 5 kilometre per hour if the distance between the two trains after 3 hours of their start in 20 kilo metres find the speed of each train

Answer 1

$\boxed{\bold{\large{Answer:}}}$

$\text{Let\:the\:two\:Trains\:be\:P\:and\:Q}$

$\text{Speed\:of\:Train\:P\:=\:xKm/hr}$

$\text{Speed\:of\:Train\:Q\:=\:(x\:+\:5)\:Km/hr}$

$\text{After\:3\:hours,}$

$\text{Distance\:traveled\:by\:P\:=\:3x\:Km}$

$\text{Distance\:traveled\:by\:Q\:=\:3(x\:+\:5)}$

$\text{By\:Distributive\:Property\:we\:get, }$

$\text{3x\:+\:15\:km}$

$\text{According\:to\:the\:Question,}$

$\text{Distance\:between\:P\:and\:Q\:is\:20\:Km}$

$\implies3x + (3x + 15) + 20 = 425 \\ \\ \implies6x + 35 = 425 \\ \\ \implies6x = 425 - 35 = 390 \\ \\ \implies \: x = \frac{390}{6} \\ \\ \implies \: x = 65 \: km \: per \: hr$

$\text{Now,}$

$\text{x\:+\:5\:=\:65\:+\:5\:=70Km/Hr}$

$\text{Thus,the\:speed\:of\:the\:Trains\:are\:65km/hr\:and\:70Km/hr\:Respectively.}$

$\boxed{\bold{\large{Hope\:it\:helps\:you!}}}$

Answer 2

Given that distance between two stations= 425 km
Let the speed of the first train be x km/hr
Then the speed of other train is (x+5) km/hr
Distance travelled by first train in 3 hours = 3 × x km/hr = 3x km 
Distance travelled by second train in 3 hours = 3× (x+5) km/hr = 3x +15 km
Also given that distance between the trains after three hours= 20
By given data 
3x + 20 + 3x+15 = 425
6x + 35 = 425
6x = 425 - 35 = 390
x = 390 / 6 = 65 km/hr 
Therefore speed of first train = x = 65 km/hr
speed of second train = x + 5 = 65 + 5 = 70 km/hr