Brain Teasers
Catching Up
Fun: (2.22)
Difficulty: (1.89)
Puzzle ID: #19152
Submitted By: lesternoronha1 Corrected By: MarcM1098
Submitted By: lesternoronha1 Corrected By: MarcM1098
Rakesh and Shyam are competing in a 100m race. Initially, Rakesh runs at twice Shyam's speed for the first fifty meters. After the 50m mark, Rakesh runs at 1/4th his initial speed while Shyam continues to run at his original speed. At what distance from the finish line does Shyam catch up with Rakesh?
Answer
Shyam catches up with Rakesh at a distance of 25m from the finish line.Let Rakesh's and Shyam's speeds be 'r' and 's' initially.
Then we have for the first 50m, Rakesh's speed = Twice Shyam's speed i.e., r = 2s.
After the 50m mark, Rakesh's speed = 1/4th his original speed = Half of Shyam's speed
i.e., r = s/2.
Now let Rakesh and Shyam meet at 'X' m from the start line, after a time 't'.
Time taken by Rakesh to cover 'X' m = Time taken by Shyam to cover 'X' m
(since they meet after having covered X m.)
Time taken by Rakesh to cover 'X'm =
(Time taken by Rakesh to cover first 50 m) + (Time taken by Rakesh to cover the remaining 'X-50' m) =
(50/2s) + ((X-50)/(s/2))
(since Rakesh's speed is 2s for first 50m and then onwards s/2)
Time taken by Shyam to cover 'X' m = (X/s)
(since Shyam ran at the same speed s throughout)
Hence
(50/2s) + ((X-50)/(s/2)) = (X/s)
25/s + ((2X-100)/s) = X/s
(25+2X-100)/s = X/s
Hence X = 25+2X-100 i.e., X = 75m
Thus Rakesh and Shyam meet at a distance of 75m from the start line.
Hence Rakesh and Shyam should be meeting from the finish line at a distance
= 100 - X = 100 - 75 = 25m
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