Question

Tuliram runs in a triathlon consisting of three phases in
the following manner. Running 12 km, cycling 24 km and
swimming 5 km. His speeds in the three phases are in the
ratio 2:6:1. He completes the race in n minutes. Later, he
changes his strategy 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 minutes
more than the earlier speed. It is also known that he has not
changed his running speed when he changes his strategy.​

Answer 1

Answer:

Let x be the ratio multiplier in the 1st case and y be the same in the 2nd case.

Hence, 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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