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Bunuel
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I would try to solve it mathematically.
Let the distance be x between home and park, and speed of dog and man be d and m respectively.
Now, it's given that the dog covers the x distance in 30 mins
So, x = 30d

Also, they meet in 10 mins. Let the distance here to be covered be y.
So, y /(d+m) = 10
y = 10d + 10m

Additionally, man covers (x-y) distance in 50 mins (dog takes 30 mins to reach and plays for 20 mins)
So, x-y = 50m
Substituing the values,

30d - 10d -10m = 50m
d = 3m

To find, the time it takes for man to cover x distance, x/m
x/m = 30*3m/m (x= 30d & d= 3m)

So, 90 mins out of which they have already be walking for 60 mins. So, they will reach the park at 10.30 AM
Alternatively, they started at 9 and walked for 90 mins so, they will reach at 10.30 AM
D
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