Runners A, B, and C run a 100-m race, each at a constant speed. Runner A takes f

Question

Runners A, B, and C run a 100-m race, each at a constant speed. Runner A takes first place, beating runner B by 10 m . Runner B takes second place, beating runner C by 12 m .

Problem 2.75 Runners A, B, and C run a 100-m race, each at a constant speed. Runner A takes first place, beating runner B by 10 m. Runner B takes second place, beating runner C by 12 m Part A By what time interval does runner A beat runner C? Express you answer as a fraction of the time that the runner A spent to finish the race. Express your answer using two significant digits tc -tA Submit My Answers Give U

Explanation / Answer

Let us assume the velocities of A,B,C be va,vb,vc

At the time when A completed 100 m we have ,

vb*(100/va) + 10 = 100 /* at this time B is 10 meters behind A and time elapsed is 100/va */

At the time when B completed 100 we have,

vc*(100/vb) + 12 = 100   /* at this time C is 12 meters behind B and time elapsed is 100/vb */

solving the above two equation we get,

vb/va = 9/10 and vc/vb = 12/10

which gives vc/va = 144/100

now, 100 *vc = 144*va = 100 m

So, vc = 1 ,va = 100/144

So, time difference is tC - tA 144-100 =44sec

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