In a kilometer race, A beats B by 1 minute. In the same race, B beats C by 30 seconds. If A beats C by 600 m, find the ratio of speeds of A and B. Please share you approach.

A ran 1000 m in the time that C ran 400 m. So, ratio of speeds of A and C is 5:2
Let the ratio of speeds of A, B and C be 5:x:2. So, speeds = 5k, xk and 2k

Time taken by B - Time taken by A = 1000/xk - 1000/5k = 60 seconds
Time taken by C - Time taken by B = 1000/2k - 1000/xk = 30 seconds
Equating for k, we get, 200*(5/x - 1)/60 = 500*(1-2/x)/30 => x = 2.5

So, speed of A : Speed of B = 5 : 2.5 = 2:1

Time taken by A: t
Time taken by B: t+60
Time taken by C: t+60+30 = t+90

A beats C by 600m and by 90 seconds. So, C runs 600m in 90 seconds.
Time taken by C to run 1000m = (1000*90)/600 = 150 seconds
Time taken by B to run 1000m = 120 seconds
Time taken by A to run 1000m = 60 seconds

Speed of A/Speed of B = Time taken by B/Time taken by A (since distance is constant, time is inversely proportional to speed
Sa/Sb= 120/60 = 2:1

In a kilometre race, P beats Q by 1 minute. Q beats R by 30 seconds. If Possible beats R by 200 Mt , find the time R takes to run the race?