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October 7th, 2019, 11:26 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 477 Thanks: 1  Explain these two questions in distance problem.
Shatabdi express left Delhi 40 min late. After covering half of the distance it increased its usual speed by 1/6 of original speed and reached Chandigarh on scheduled time. Find usual time (in min) taken by Shatabdi express to cover complete journey. Solution: Speed Ratio; 6 : 7 Time ratio; 7 : 6 Difference in time ratio;1 corresponds to 40 min. 7*40 = 280. 280*2 = 560 min How Difference in time ratio corresponds to 40 min? Why multiplying 280 with 2 in last step? 
October 8th, 2019, 01:16 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,035 Thanks: 2271 
It's necessary to assume that the usual speed was the same for both halves of the journey, so that the usual time was the same for both halves of the journey. The change in speed for the second half of the journey multiplied the time needed for it by 6/7, i.e. reduced it by 1/7 of its usual value. As the reduction was 40 minutes (because it made up for the express having left Delhi 40 minutes late), the usual time was 280 minutes. Hence the usual time for the first half of the journey was also 280 minutes, and so the usual time for the complete journey was 560 minutes. According to Google, the complete journey ought to take about 200 minutes. 

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