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,travels 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. Hamid would have caught him after 3 hours.find the speed of hamid and joseph.

Answer 1

Let the speed of Joseph = xkm/h

Let the speed of Hamid = ykm/h

When approaching one another, combined speed = (x+y)km/h

Time taken to meet = 30/(x+y) = 1/3  (20 minutes = 1/3 hours)

x+y = 90 ------ (i)

When moving in opposite direction, combined speed = (x-y)m/h

Time taken for Hamid to catch up = 30/(x-y) = 3

x-y = 10 ---- (ii)

Solving (i) and (ii) simultaneously


x+y = 90
x-y = 10
_______
2x = 80
x = 40

y = 50


∴ Speed of Joseph = 40km/h

Speed of Hamid = 50km/h

Answer 2

Hi ,

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/hr

they meet in 20 minutes = 20/60 hr = 1/3hr

Relative speed = distance/ time

x + y = 30/ ( 1/3 )

x + y = 90 ---- ( 1 )

ii ) when they travel in same direction ,

relative speed = ( x - y ) km/hr

they 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 = 100/2

x = 50

put x = 50 in equation ( 1 ), we get

y = 40

Therefore ,

speed of the Hamid = x = 50 km/hr

speed of the Joseph = y = 40 km/hr

I hope this helps you.

: )