Question

question no 7
a goods train leaves a station at 6 pm followee by express train 8 pm which travels 20 km /hr faster . the express train arive 36 min before goods train . if distance is 1040 km . assuming speed of both temain constant . calculate speed of both

Answer 1

Let the speed of the goods train be
'x' km/hr
Then, speed of express train=(x+20) km/hr
Goods train leaves a station at 6pm and express train leaves the station at 8pm
also express train reaches its destination 36min before goods train.
We known that,
Time taken = distance covered /speed
Total distance=1040km
Time taken by goods train to cover
1040 km=1040/x

Time taken by express train to cover 1040 km=1040/(x+20)
As per given condition we have,
1040/x=1040/(x+20)+2(36/60)

1040/x-1040/(x+20)=2(3/5)

(1040x+20800-1040x)/(x²+20x)=13/5

13x²+260x=104000

x²+20x-8000=0

x²+100x-80x-8000=0

x(x+100)-80(x+100)=0

(x-80)(x+100)=0

x=80 (or) x=-100
Here x>0
Therefore x=80

Hence speed of goods train=80 km/hr
and speed of express train=100 km/hr.

Answer 2

Answer:

Let the speed of goods train be x km/hr. So, the speed of the express train will be (x + 20) km/hr.

Distance = 1040 km

We know: Time = distance/speed

Time taken by goods train to cover a distance of 1040 km = $\frac{1040}{x}$ hrs

Time taken by express train to cover a distance of 1040 km = $\frac{1040}{x+20}$ hrs

It is given that the express train arrives at a station 36 minutes before the goods train. Also, the express train leaves the station 2 hours after the goods train. This means that the express train arrives at the station (36/60 + 2) hrs = 13/5 hrs before the goods train.

$Therefore,\frac{1040}{x} -\frac{1040}{x+20}=\frac{13}{5}$

⇒$\frac{1040x+20800-1040x}{x(x+20)}=\frac{13}{5}$

⇒$\frac{20800}{x^{2}+20x }=\frac{13}{5}$

⇒$\frac{1600}{x^{2}+20x}=\frac{13}{5}$

⇒$5(1600)=x^{2}+20x$

⇒$8000=x^{2}+20x$

⇒$x^{2}+20x-8000=0$

⇒$x^{2}+100x-80x-8000=0$

⇒$x(x+100)-80(x+100)=0$

⇒$(x+100)(x-80)=0$

⇒ $x-80=0\\x+100=0$

⇒$x=80,x=-100$

Since the speed cannot be negative. So, x = 80.

Thus, the speed of the goods train is 80 km/hr and the peed of the express train's speed is 100 km/hr.