Math, asked by ankitdwivediii, 3 months ago

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

Answered by Anonymous
17

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

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