Q5 of 23 Page 1

Attempt any two sub-questions from the following:

From the same place at 7 a.m. A started walking in the north at the speed of 4 km/hr. After 1 hour B started cycling in the east at a speed of 8 km/hr. At what time will they be at a distance of 20 km apart from each other?


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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