Question

A train covers a distance of 90 km at a uniform speed . It would have taken 30 min less if the speed had been 15km/hr more . Calculate the original duration of journey .

Answer 1

Heya.......!!!!

This question can be easily solved by making equations .



=> Let the speed of train be x km/hr .

As we have to calculate the duration of journey ( i.e time ) So ,, time = D/S

1.) Time = 90/x

2.) if 30 min less then speed would 15km/hr more . Time = 90/( x + 15 ).

According to the question :

=> 90/x - 90/( x + 15 ) = 1/2

=> x^2 + 15x - 2700 = 0

Solving this quadratic equation , we get x = -60 or 45.

as the speed can't be negetive so reject - 60 .

We get x = 45 km/hr .

Time = Distance / Speed

➡ 90/45 =>> 2 hours .

♦ Original duration of journey = 2 hr .

Hope It Helps You ^_^

Answer 2

Hey.

let the initial speed of train be x km / h

so, time taken= D/s =90/x hr

new speed=x+15
new time = 90/x -15/60 hr =90/x-1/4 hr
also new time = 90/x+15
equating both new times we get
90/x+15 = 90/x -1/4
or, 90/x+15 =(90×4-x)/4x
or, 90×4x =(360-x)×(x+15)
or, 360x =360x -360×15-x^2-15x
or, x^2+15x +360×15=0
so, get x and then put x in 90/x to get original time.

Thanks