Question
Tuliram runs in a triathlon consisting of 3 phases in the following manner.running 12 km,cycling 24 kkm and swimming 5 km.his speeds in the 3 phases are in the ratio 2:6:1.he completes the race in n minutes.later he changes his stratgey so that the distances he covers in each phase are constant but his speeds are now in the ratio 3:8:1.the end result is that he completes the race taking 20 mins more than the earlier speed.it is also known that he has not changed his running speed when he changes his strategy.
Let x be the ratio multiplier in the 1st case and y be the same in the 2nd case.
ReplyDeleteHence, in 1st case:
Running speed = 2x
Cycling speed = 6x
Swimming speed = x
Similarly, in 2nd case:
Running speed = 3y
Cycling speed = 8y
Swimming speed = y
Given that, running speed is same. Hence,
2x = 3y...........................................................(1)
Now, Time = Distance/Speed
Therefore,
Case 1:
n/60 = 12/(2x) + 24/(6x) + 5/x.............(since n is in minutes)
=> n/60 = 6/x + 4/x + 5/x
=> n/60 = 15/x
=> n = 900/x.....................................................(2)
Case 2:
(n+20)/60 = 12/(3y) + 24/(8y) + 5/y
=> (n+20)/60 = 4/y + 3/y + 5/y
=> (n+20)/60 = 12/y
=> n+20 = 720/y...................................................(3)
Replace y=2x/3 from eq.(1) in eq.(3)
Hence, (3) becomes,
n+20 = 1080/x
20 = 1080/x - 900/x...................................(From (2))
20 = 180/x
=> x = 9
=> y = 6
Question Incomplete!!
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