A train starts form Delhi at 8:00 am. After 6 hrs there was breakdown in the train, due to which it travels 3/4 of its normal speed and hence becomes 40 minutes late. If the breakdown would be 20km further then it will 30 minute late only. Find the distance from delhi to agra?
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