Question

Two trains leave the railway station at a same time. The first train travels west and second train travelled north. The first train travels 5 kmph faster than second train. If after two trains they are 50 km apart. Find the speed of each train?

Answer 1

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

The speed of the first train = x+5 km/hr

Distance covered after two hours by the first train is 2(x+5) km.

Distance covered by the second train after two hours is 2x km.

(2x)^2 + 4(x+5)^2=(50)^2 (Using pythagoras theorem)

Solve 

We get x=-20 and x=15

since, speed can't be negative

The speed of second train is 15km/hr

The speed of the first train = 15+5=20km/hr

Answer 2

$\huge \sf \color{purple}{\underline{\underline{Answer}}} :$

Speed of first train is 20 Km/h and speed of 2nd train is 15 Km/h

$\huge \sf \color{purple}{\underline{\underline{Solution}}}:$

➣ Let the 2nd train travel at X km/h

➣Then, the speed of a train is (5 +x) Km/hour.

➣ let the two trains live from station M.

➣ Distance travelled by first train in 2 hours

$\sf \boxed{\colorbox{skyblue}{Distance=speed×time}}$

= MA = 2(x+5) Km.

➣ Distance travelled by second train in 2 hours

= MB = 2x Km

$\sf \color{brown}{By \: Phythagoras \: theorem }$ AB²= MB²+MA²

⟹ 50²=(2(x+5)²+(2x)²

⟹ 2500 = (2x+10)² + 4x²

⟹8x² + 40x - 2400 = 0

⟹x² + 5x - 300 = 0

⟹x² + 20x -15x - 300 = 0

⟹x(x + 20) - 15(x + 20) = 0

⟹ (x + 20)(x -15) = 0

$\sf \boxed{\colorbox{lightgreen}{x=15 \: or \: 20}}$

Taking x = 15 , the speed of second train is 15 Km/h and speed of first train is 20 Km/h