Question

Amaravati Express after travelling 125 km met with an accident due to which it proceeds at 75% of it's original speed and arrived at its destination 35 minutes late. Had the accident took place 30 km further, then the train would have been 25 minutes late. Amaravati Express passes a pole with its original speed in 45 seconds and crosses Lucknow Express which is 20% more longer than Amaravati Express, coming in opposite direction in 0.9 minutes. Find the time taken by Lucknow Express to cover the total distance travelled by Amaravati Express
A. 4.2 hours
B. 4.4 hours
C. 4.6 hours
D. 4.8 hours
E. None of these​

Answer 1

4.6 hrs is the time taken by Lucknow Express to cover the total distance travelled by Amaravati Express

Step-by-step explanation:

Let say Total distance = D km

Amravati original Speed =  A km/hr

Original Time = D/A

Time taken for 125  km =125/A  hr

Reduced Speed = (75/100)A = 3A/4 km/Hr

Time Taken =  (D - 125)/(3A/4)  =  (4D - 500)/3A hr

125/A  + (4D - 500)/3A  =  D/A  + 35/60

=> 7500  + 80D - 10000 = 60D  + 35A

=> 20D = 35A + 2500

=> 4D = 7A + 500

Had the accident took place 30 km further  train would have been 25 minutes late.

=> 155/A  + 4(D - 155)/3A  =  D/A  + 25/60

=> 9300  + 80D - 12400 = 60D + 25A

=> 20D = 25A + 3100

=> 4D = 5A + 620

7A + 500 =  5A + 620

=> 2A = 120

=> A = 60

Amravati original Speed =  60 km/Hr

4D = 7A + 500

=> 4D = 920

=> D = 230

Distance = 230  km

Amaravati Express passes a pole with its original speed in 45 seconds

Distance covered in 45 sec  =  60 * 45/3600  = 0.75 km = 750 m

Length of Amaravati Express Train = 750m = 0.75 km

Lucknow Express which is 20% more longer = 750 + (20/100)750 = 900 m

= 0.9 km

0.75 + 0.9 = 1.65 km

Time = 0.9 mins = 9/600 hrs

Speed = 1.65/ (9/600)  = 110 km/hr

Speed of lucknow Express = 110 - 60 = 50 km/hr

the time taken by Lucknow Express to cover the total distance travelled by Amaravati Express = 230 / 50

= 23/ 5 hrs

= 4.6 Hrs

Learn more:

एक 500 मीटर लंबी रेलगाड़ी 60 किलोमीटर प्रति घंटा ...

https://brainly.in/question/8136340

After travelling 3 hours a train meets with an accident due to this it ...

https://brainly.in/question/8989697

A train met with an accident 60km away from station a. It completed ...

https://brainly.in/question/7348096