Three friends cycled along a circular track of radius 105m sunil started 2s after ramesh but he was 1m/s faster than ramesh rameshstarted 2s after rikshith but he was min faster than him if sunil won the race what could have been rikshit's speed
Answers
Rikshit speed = 16.67 m/s (50/3 m/s)
Step-by-step explanation:
Let say rikshith Speed = R m/s
Ramesh Speed = R + 1 m/s
Sunil Speed = R + 2 m/s
Let say Sunil took t sec to complete race
then ramesh took > t - 2 secs
rikshith took > t - 4 sec
(R+2)t = 105 * 2 π = 105 * 2 * 22/7 = 660
=> Rt =660 - 2t
=> t = 660/(R + 2)
(R + 1)(t + 2) < 660
(R)(t + 4) < 660
(R + 1)(t + 2) < 660
=> Rt + t + 2R + 2 < 660
=> 660 - 2t + t + 2R + 2 < 660
=> 2R - t + 2 < 0
=> 2R -(660)/(R + 2) + 2 < 0
=> 2R² + 4R - 660 + 2R + 4 < 0
=> 2R² + 6R - 656 < 0
=> 2R² + 6R < 656
=> R² + 3R < 328
=> ( R + 3/2)² - 9/4 < 328
=> ( R + 3/2)² < 1321/4
=> R + 3/2 < 18.173
=> R < 16.673
(R)(t + 4) < 660
=> Rt + 4R < 660
=> 660 - 2t + 4R < 660
=> -2t + 4R < 0
=> -2 * 660/(R + 2) + 4R < 0
=> -1320 + 4R² + 8R < 0
=> 4R² + 8R < 1320
=> R² + 2R < 330
=> (R + 1)² - 1 < 330
=> (R + 1)² < 331
=> R + 1 < 18.19
=> R < 17.19
Rikshit speed = 16.67 m/s
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