Three persons A, B and C travel from point P to Q along three different paths as shown below. Person A travels along semi-circular path, person B travels in straight line path between P and Q and person C travels along the path PRQ. If the time taken by A, B and C is related as 2tA = 3tB = 5tc, then relation between their speeds are given by.
Answers
Given : Three persons A, B and C travel from point P to Q along three different paths
Person A travels along semi-circular path
person B travels in straight line path
person C travels along the path PRQ
time taken by A, B and C is related as 2tA = 3tB = 5tC,
To Find : relation between their speeds
Solution:
2tA = 3tB = 5tC = 30K
Time taken by A , B & C are :
=> tA = 15K
=> tB = 10K
=> tC = 6K
A travels along semi-circular path, => Distance = πR
R = Radius = Diameter/2 = 10/2 = 5 m
=> Distance = π5
Time by A = 15K
=> Speed = π/3K
B travels in straight line path between P and Q
PQ = 10 m
=> Distance = 10 m
Time by B = 10K
=> Speed = 1/K
C travels along the path PRQ.
PR + RQ = 8 + 6 = 14 m
Time by C = 6K
=> Speed = 14/6K = 7/3K
π/3K : 1/K : 7/3K
=> π : 3 : 7
relation between their speeds π : 3 : 7
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