Answer :

Let O be the starting point.

A walks towards North with 4 km/h and B walks towards East at 8 km/h after 1 hour.

Let A reaches point A and B reaches point B when they are 20 km apart.

Let the travel time of B = x hours

Travel time of A = (x + 1) hours

OA = speed × time = 4(x + 1) km

OB = 8x km

Now by Pythagoras theorem,

AB^{2} = OA^{2} + OB^{2}

⇒ 20^{2} = [4(x + 1)]^{2} + (8x)^{2}

⇒ 400 = 16(x^{2} + 1 + 2x) + 64x^{2}

⇒ 25 = x^{2} + 2x + 1 + 4x^{2}

⇒ 5x^{2}+ 2x – 24 = 0

⇒ 5x^{2} – 10x + 12x – 24 = 0

⇒ 5x(x – 2) + 12(x – 2) = 0

⇒ (x – 2) (5x + 12) = 0

⇒ x = 2 or x = -12/5

∴ travel time of B = x hours = 2hours

Travel time of A = (x + 1) hours = 2 + 1 hours = 3 hours

Hence, at 10:00 am they will be 20 km apart.

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