Question

places A and B are 30 km apart and they are on a straight road. Hamid travels from A to B on bike. At the same time Joseph starts from B on bike, travel towards A . They meet each other after 20 minutes. If Joseph would have started from B at the same time but in the opposite direction (instead of towards A) Hamid would have caught him after 3 hours. Find the speed of Hamid and Joseph.

Answer 1

Let the speed of Hamid be ' x ' km/hr and 
The speed of Joseph be ' y ' km/hr

Total Distance from A to B = 30km
according to the problem given ,
i ) when Hamid and Joseph travel in opposite
direction , then relative speed = ( x + y ) km/hrthey meet in 20 minutes = 20/60 hr = 1/3hrRelative speed = distance/ time
x + y = 30/ ( 1/3 )x + y = 90 ---- ( 1 )
ii ) when they travel in same direction , 
relative speed = ( x - y ) km/hrthey meet in 3 hr 
relative speed = distance/time 
x - y = 30/3

x - y = 10 ----( 2 )add equations ( 1 ) and ( 2 ) we get,2x = 100
x = 100/2x = 50put x = 50 in equation ( 1 ), we get 
y = 40 
Therefore ,speed of the Hamid = x = 50 km/hrspeed of the Joseph = y = 40 km/hr
I hope this helps you.