Question

A train travels a distance of 300km at constant speed.if the speed of train is increased by 5km an hour the journey would have to taken 2 hr less find the original speed of the train

Answer 1

LET THE SPEED OF TRAIN BE S.

THEN,

TIME = DISTANCE / SPEED

TIME = 300 / S

NOW, ACCORDING TO THE SECOND CASE,

IF SPEED IS INCREASED BY 5.

THAT IS,

NEW SPEED = S + 5

IT WOULD TAKE 2 HOUR LESS,

THAT MEANS,

TIME = 300 / S - 2

TIME = 300 - 2S / S

WE CAN OBSERVE THAT THE DISTANCE IN BOTH CASES ARE EQUALS,

SO,

NEW SPEED X NEW TIME = SPEED X TIME

(S+5)(300-2S/S)=S(300/S)

(300S-2S²+1500-10S)/S=300

300S-2S²+1500-10S=300S

-2S²+1500-10S = 0

-S²+750-5S = 0

-S²-5S+750 = 0

IF YOU SOLVE THE ABOVE EQUATION YOU WILL GET S1 = - 30 AND S2 = 25

HENCE, THE SPEED OF A BODY CANNOT BE NEGATIVE SO THE SPEED OF TRAIN WILL BE 25 KMPH.

PLZ MARK IT AS BRAINLIEST ANSWER AND DROP A ♥

Answer 2

Answer:

Let the original speed of the train be y km / hr .

A.T.Q.

$\displaystyle{\frac{300}{y} -\frac{300}{y+5} =2 }$

300 ( y + 5 ) - 300 y = 2 y ( y + 5 )

y² + 5 y - 750 = 0

y² + 30 y - 25 y - 750 = 0

( y + 30 ( y -25 ) = 0

y = - 30 or y = 25

Since , speed of train can't be negative .

Therefore , the original speed of the train is 25 km / hr .