Question

The ratio of speeds of a goods and passengers train is 9:14 in same direction..If the passenger train crosses the goods train in 1 minute 25 sec while a passenger in passenger train observes that he crosses the goods train in 35 sec..If the sum of lengths goods and passenger train is 1326 metres then find difference between their length..??​

Answer 1

Answer:

Difference between their length = 234 metres

Step-by-step explanation:

Let's assume that, speed of the goods train is 9z metres/second

∴ speed of the passenger train is 14z metres/second

Let's also assume that, the length of the goods train is x metres and the length of the passenger train is y metres.

In 1 minute 25 seconds, i.e. in 85 seconds, the passenger train crosses the goods train, the distance covered in the process = Length of Goods Train + Length of Passenger Train + The distance the Goods train covers during this passing duration.

= x + y + (9z times 85) = 1326 + 9z.85

Now, the passenger train is moving at the speed of 14z

∴ 14z times 85 = 1326 + 9z. 85

∴ 85(14z - 9z) = 1326

∴ z $=\frac{1326}{5x85}$ $=\frac{78}{25}$

And a passenger in passenger train observes that, he crosses the goods train in 35 seconds.

During this period of time, the distance the passenger train covers:

= 14z times 35

= the length of the good train + the distance the goods train covers.

= x + (9z times 35)  

Putting the value of z:

x + (9 . 35 . $\frac{78}{25}$) = 14 .35 . $\frac{78}{25}$

∴ x = 5 . 35. $\frac{78}{25}$ = 7 . 78 = 546 metres

∴ y = 1326 - 546 = 780 metres

∴ y - x = (780 - 546) metres = 234 metres

Answer 2

Answer:

Difference between their length = 234 metres

Step-by-step explanation:

Let's assume that, speed of the goods train is 9z metres/second

∴ speed of the passenger train is 14z metres/second

Let's also assume that, the length of the goods train is x metres and the length of the passenger train is y metres.

In 1 minute 25 seconds, i.e. in 85 seconds, the passenger train crosses the goods train, the distance covered in the process = Length of Goods Train + Length of Passenger Train + The distance the Goods train covers during this passing duration.

= x + y + (9z times 85) = 1326 + 9z.85

Now, the passenger train is moving at the speed of 14z

∴ 14z times 85 = 1326 + 9z. 85

∴ 85(14z - 9z) = 1326

∴ z $=\frac{1326}{5x85}$ $=\frac{78}{25}$

And a passenger in passenger train observes that, he crosses the goods train in 35 seconds.

During this period of time, the distance the passenger train covers:

= 14z times 35

= the length of the good train + the distance the goods train covers.

= x + (9z times 35)  

Putting the value of z:

x + (9 . 35 . $\frac{78}{25}$) = 14 .35 . $\frac{78}{25}$

∴ x = 5 . 35. $\frac{78}{25}$ = 7 . 78 = 546 metres

∴ y = 1326 - 546 = 780 metres

∴ y - x = (780 - 546) metres = 234 metres