Given that A beats B by 50 sec.
Means A reached finish point 50 sec earlier than B(or B takes 50 sec more to complete the race) in one kilometer race.
Hence Time req for B - Time req for A = 50sec
$\frac{D_{B}}{S_B} - \frac{D_A}{S_A} = 50$ sec
$\frac{1000}{S_B} - \frac{1000}{S_A} = 50$ sec -------------(1)
Now, A beats C by 450 m. (Means when A reaches finish line, C is 450 meters behind him)
Means in the same time A reaches 1000m (race is KM race) and C reaches 550m
$\frac{D_{A}}{S_A} = \frac{D_C}{S_C}$ (Equating their times)
$\frac{1000}{S_A} = \frac{550}{S_C}$ ------------------(2)
Now B beats C by 40s. Means C takes 40s more to reach finish line
hence Time req for C - Time req for B = 40sec
$\frac{D_{C}}{S_C} - \frac{D_B}{S_B} = 40$ sec
$\frac{1000}{S_C} - \frac{1000}{S_B} = 40$ sec --------------(3)
Now by Adding equation 1 and 3
$\frac{1000}{S_C} - \frac{1000}{S_A} = 90$ sec ---------------(4)
Substitute 2 in equation 4
$\frac{1000}{S_C} - \frac{550}{S_C} = 90$ sec
$\frac{450}{S_C} = 90$ sec
Sc = 5 m/s
Hence, time to reach 1 KM = $\frac{1000m}{5m/sec} = 200sec$
