I respect time, so I save it
One month ago, I had to go to my home(dehradun), from delhi, which is 6 hours journey. I had my train in the morning at 8:00 hrs, but however I reached at Delhi railway station two hours early I.e. at 6:00 hrs. Now as I respect time I took a train at 6:00 hrs only for my home, that train was a bit faster than the train that I had to take at 8:00 hrs and therefore I reached Dehradun 3 hours earlier than scheduled. Then I called my driver, and asked him to pick me up, he said me, "Sir, I am on schedule and have already left from the home to pick you up."
Now again to save time I started walking towards my house at a constant speed of 6 kmph. I met my driver in the way and we reached at home 1 hour earlier than scheduled. Assuming that the driver drives vehicle at a constant speed "x" . Find the sum of "x" and "d" (distance between Dehradun railway station and my home).
This problem is original.
The answer is 120.
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1 solution
The hint in the question is the statement of the driver, I.e. it takes three hours for the driver to reach the railway station from my home and vice versa if he drives with constant speed of "x" that is total of 6 hrs.Now we reached 1 hour earlier than scheduled. That means the driver met me in the way after two and half hours as
2.5 hrs from home to the meeting spot., and
2.5 hrs from meeting spot to home. That total up to 5 hrs, It also means that:
(6×(5÷2)) + (x × (5÷2)) = d.
From this equation I can see that the distance covered by me was 15 kms. And me and my driver covered distance in the ratio 1:5, as my driver instead of driving vehicle for 3 hrs in one direction drove it for 2.5 hrs, that means he covered (5/6) of the total distance. Rest was covered by me, so from here we got distance as 90 kms. Now the speed can be calculated by substituting the value of distance(d) in the above equation. And that comes out to be 30 kmph. Total sum of both i.e. 30+90= 120