a train starts from Delhi at 8 am towards allahabad after 6 hr there was a breakdown in the train due to which it travels 2/3 of its normal speed and hence become 40 min late. if the breakdown would be 60 km further than it become 40 minute late only. find the distance of that route ?
Answers
Answer:
Distance = 320 km
Step-by-step explanation:
Let Say Normal Speed of Train = S km/Hr
Speed after Breakdown = 3S/4 km/Hr
Let say Distance between Delhi & Agra = D
Time Taken at Normal Speed = D/S
Distance traveled in 6 hr = 6S km
Distance remained = D - 6S
Time taken with reduced speed for remaining Distance = (D-6S)/(3S/4)
= 4(D-6S)/3S
6 + 4(D-6S)/3S = D/S + 2/3 (40 min late = 40/60 hr = 2/3hr Late)
Multiplying by 3S on both sides
18S + 4(D-6S) = 3D + 2S
=>18S + 4D -24S = 3D + 2S
=>4D - 6S = 3D + 2S
=> D = 8S
=> D/S = 8
Time taken at Normal Speed = 8 hr
Distance travelled in 6 hr was 6S = 6D/8 = 3D/4 Km
Breakdown after 20 km
Now break down happened 3D/4 + 20 km
Remaining Distance = D - (3D/4 +20) = D/4 - 20
Time taken
= ((3D/4) + 20)/S + ((D/4) -20)/(3S/4) = 8.5 ( 30 min late , normal time = 8 hr)
=> ((3D/4) + 20)/S + 4((D/4) -20)/(3S) = 8.5
multiplying by 3S both sides
=> 9D/4 + 60 + D - 80 = 25.5S
=> 9D + 240 + 4D - 320 = 102S
=> 13 D = 102S + 80
=> 13 D = 102(D/8) + 80
=> 104D = 102D + 640
=> 2D = 640
=> D = 320 km