On average, Exante Express trains are 50 km/hr faster than Paral passenger trains. A Paral passenger train requires 60% more time than an Exante train to travel 1800 km from Matsay to Rawindi.

Calculate the average speed of each train. Also, calculate the time it takes for each train to complete the journey.

V − a v er a g e s p ee d o f E x an t e E x p ress t r ain t − t r a v e l t im e o f E x an t e E x p ress t r ain V = t S ​ an d V − 50 = t + 60% t S ​ = 1.6 t S ​ an d S = 1800 V = t 1800 ​ an d V − 50 = 1.6 t 1800 ​ ⇒ t 1800 ​ − 50 = t 1125 ​ / ⋅ t 1800 − 50 t = 1125 ⇒ 50 t = 1800 − 1125 ⇒ 50 t = 675 / : 50 t = 13.5 [ h ] = 13 [ h ] 30 [ min ] 1.6 t = 21.6 [ h ] = 21 [ h ] + 0.6 ⋅ 60 [ min ] = 21 [ h ] 36 [ min ]
V = t 1800 ​ = 13 , 5 1800 ​ = 133 3 1 ​ [ km / h ] ≈ 133.3 [ km / h ] V − 50 ≈ 83.3 [ km / h ]
A n s . a v er a g e s p ee d o f E x an t e E x p ress t r ain i s 133.3 km / h , t r a v e l t im e o f E x an t e E x p ress t r ain i s 13 h 30 min ; a v er a g e s p ee d o f P a r a l p a sse n g er t r ain i s 83.3 km / h , t r a v e l t im e o f P a r a l p a sse n g er t r ain i s 21 h 36 min

Answered by kate200468 | 2024-06-10

We can solve this problem using a system of equations. Let's say the average speed of the Paral passenger train is x km/hr. Then, the average speed of the Exante Express train would be (x + 50) km/hr.
From the given information, we know that the Paral passenger train requires 60% more time than the Exante train to travel 1800 km. So, we can set up the equation:
x + 0.6x = 1800/(x + 50)
Simplifying the equation:
1.6x = 1800/(x + 50)
Multiplying both sides by (x + 50):
1.6x(x + 50) = 1800
1.6x^2 + 80x - 1800 = 0
Now, we can solve this quadratic equation for x using the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
Plugging in the values, we get:
x = (-80 ± √(80^2 - 4(1.6)(-1800)))/(2(1.6))
x = (-80 ± √(6400 + 11520))/(3.2)
x = (-80 ± √(17920))/(3.2)
x ≈ (-80 ± 133.86)/(3.2)
Based on the nature of the problem, we can discard the negative value. Hence, x ≈ (-80 + 133.86)/(3.2) = 53.71 km/hr.
Therefore, the average speed of the Paral passenger train is approximately 53.71 km/hr, and the average speed of the Exante Express train is 53.71 + 50 = 103.71 km/hr.
To calculate the time taken for each train for the journey, we divide the distance (1800 km) by their respective speeds:
Time taken for Paral passenger train = 1800 km / 53.71 km/hr ≈ 33.51 hours
Time taken for Exante Express train = 1800 km / 103.71 km/hr ≈ 17.36 hours

Answered by Burger1123 | 2024-06-19

The average speed of the Exante Express train is 200 km/hr, taking 9 hours for the journey. The Paral passenger train has an average speed of 150 km/hr, requiring 14.4 hours to complete the same trip.
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Answered by kate200468 | 2024-11-01