if A started walking in north at speed of 5kmph at 7:00 am and after 1 hour B started cycling towards east at speed of 16 kmph. Then at what time they will be at distance of 52 km from each other.
+33616 After t hours A will have walked 5t km north.
After t hours B will have cycled 16(t-1) km east.
The distance between them is given by Pythagoras: sqrt( 52t2 + 162(t-1)2 ) → sqrt(281t2 - 512t + 256) km
So we have: sqrt(281t2 - 512t + 256) = 52
Square both sides
281t2 - 512t + 256 = 2704
281t2 - 512t - 2448 = 0
(281t + 612)(t - 4) = 0
The only positive solution is t = 4 hours.
Hence they are 52 km apart at 7 + 4 → 11 am.
