Question

Amy and pamy are running a 200 metre race they both start from the same point at same time Tammy beats Ami by 10 second if any runs twice as fast as a normal running speed Ami beats pay me by 15 seconds how much headstart should pamy give a me so that the race and in that heat if both run at the usual speed​

Answer 1

Given : Ami and pammy are running a 200 metre race they both start from the same point at same time Pammy beats Ami by 10 second if ami runs twice as fast as a normal running speed Ami beats pammy by 15 seconds

To find : Pammy Should give Ami headstart at usual speed to complete race at time

Solution:

Distance = 200 m

Speed of pammy  = P m/s

Time taken by pammy = 200/P  sec

Time taken by Ami = 200/P + 10  sec

= (200 + 10P)/P  sec

Speed of Ami = 200/ ((200 + 10P)/P)

= 200P/(200 + 10P)

= 20P/(20 + P)  m/s

Ami runs twice as fast as a normal running speed  

Ami = 2 * 20P/(20 + P)  = 40P/(20 + P)   m/s

Time taken by  Ami   = 200/(40P/(20 + P)) = 5(20 + P)P  sec

Ami beats pammy by 15 seconds

5(20 + P)P  + 15  = 200/P  

=> 100 + 5P + 15P = 200

=> 20P = 100

=> P = 5

Speed of pammy  = 5 m/s

Speed of Ami =  20P/(20 + P) = 4 m/s

At usual speed 10 secs head start to given to Ami

Distance covered by Ami in 10 secs = 10 * 4 = 40 m

40 m Head start to be given by Pammy to Ami

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