a train goes from stations a to b. one day there is a technical problem at the very beginning of the journey & hence the train travels at 3/5 of it's original speed and so it arrives 2 hours late. had the problem occurred after 50 miles had been covered, the train would have arrived 40 min earlier(i.e., only 120-40 = 80 min late). what is the distance between the 2 stations?
Answers
the distance between the 2 stations = 150 miles
Step-by-step explanation:
Let say Distance between stations = D miles
Speed of train = 5S miles / hr
Normal Time = D/5S hr
train travels at 3/5 of it's original speed
=> Speed = (3/5)5S = 3S miles /hr
Time taken at (3/5) speed = D/3S hrs
D/3S = D/5S + 2
multiplying by 15S both sides
=> 5D = 3D + 30S
=> 2D = 30S
=> D = 15S
Time taken when problem occurred 50 miles after
then Time taken = 50/5S + (D - 50)/3S hrs
50/5S + (D - 50)/3S = D/5S + 80/60
=> 10/S + (D - 50)/3S = D/5S + 4/3
multiplying by 15S both sides
=> 150 + 5D - 250 = 3D + 20S
=> 2D = 20S + 100
=> D = 10S + 50
15S = 10S + 50
=> 5S = 50
=> S = 10
D = 15S = 15 * 10 = 150 miles
the distance between the 2 stations = 150 miles
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