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
Answers
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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