Question

Two trains X and Y start from a railway station at the same time.The X train travels due west and the Y train due north. the X train travels 5km/hr faster that the Y train.If after two hours , they are 50 km apart, find the average speed of two trains.

Answer 1

Answer:

17.5 km/Hr

Step-by-step explanation:

Two trains X and Y start from a railway station at the same time.The X train travels due west and the Y train due north. the X train travels 5km/hr faster that the Y train.If after two hours , they are 50 km apart, find the average speed of two trains.

Let say speed of Y train = Y km/Hr

X train travels 5km/hr faster that the Y train

Speed of X train = Y + 5 km/Hr

Distance traveled by X Train in 2hrs = 2(Y + 5)  km   West

Distance traveled by Y Train in 2hrs = 2Y km   North

North & West are perpendicular  to each other

Distance between train² = North Distance² + West Distance²

=> 50² = (2Y)² + (2(Y+5))²

=> 25² = Y² + (Y+5)²

=> 625 = Y² + Y² + 25 + 10Y

=> 2Y² + 10Y - 600 = 0

=> Y² + 5Y - 300 = 0

=> Y² + 20Y - 15Y -300 = 0

=> Y(Y +20) -15(Y +20) = 0

=> (Y -15) (Y +20) = 0

Y = 15

Speed of Y Train = 15 km/Hr

Speed of X train = 20 km/Hr

Average speed of both Train =  (15 + 20)/2 = 17.5 km/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