Q. 5 C4.4( 7 Votes )

# Attempt any two s

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,

AB2 = OA2 + OB2

202 = [4(x + 1)]2 + (8x)2

400 = 16(x2 + 1 + 2x) + 64x2

25 = x2 + 2x + 1 + 4x2

5x2+ 2x – 24 = 0

5x2 – 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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