self doubt

Question

Find time of second meeting of 2 ducks moving at 10km/hr and 18km/hr in opposite direction along the circumference of a circular pond. Initailly they are present at any pair of diametrically opposite points. radius of pond is 7km

Answer 1

let the two ducks be a(10 km/h) and b(18 km/h).

given that radius of pond= 7km . so circumference = 44 km.

they move in opposite direction means one clockwise and one anti clockwise and as they are diametrically opposite.

let a travels x km before they meet so b will travel (22-x) km.

as time will be equal so making equation 1 for meeting first time.

=> ( x/10)=((22-x)/18)

=>x=(55/7)

=> t1(time for 1st meeting) =speed of a *time = 0.78hr

now for meeting 2. let a travels y distance b travels (44-y).

==> (y/10)=((44-y)/18)

=>y=110/7

=>time taken(t2) = speed of a *time = 110/70 = 1.57hr

total time = t1+t2 = (.78 +1.57)= 2.35hrs

Comments

Won't t2 include t1 as well?

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they meet first time at .78hrs and second time at 1.57hrs so total time =2.35 hrs