Question

place a and b are 30 km apart and they are on a straight road. hamid travel from a to b on bike. at the same time Joseph start 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 hamid would have caught him after 3 hours. find the speed of hamid and Joseph

Answer 1

• The relative speed of two moving bodies is the rate at which the distance between them increases or decreases.
•For two bodies moving in the same direction ,relative speed = difference of their speeds.
•For two bodies moving in opposite directions, relative speed = sum of their speeds.

SOLUTION :
Let the ' x ' km/h be the speed of Hamid and ' y ' km/h be the speed of Joseph.

GIVEN :
Total Distance from A to B = 30 km

ATQ,

i ) when both of them travel in opposite direction , then their relative speed = (x + y ) km/h

they meet in 20 minutes = 20/60 h = 1/3h
[ 1 minutes = 1/60 h]

Relative speed = Distance/ Time

x + y = 30 / ( 1/3 )

x + y = 30 ×3

x + y = 90 ………………. (1)

ii ) when both of them travel in same direction , then their relative speed = ( x - y ) km/h
they meet in 3 hr

Relative speed = Distance/Time

x - y = 30/3

x - y = 10 ………………( 2 )

On Adding eqs ( 1 ) and ( 2 ),

x + y = 90
x - y = 10
----------------
2x = 100
----------------

x = 100/2

x = 50

put x = 50 in eq ( 1 ),

x + y = 90
50 + y = 90
y = 90 - 50
y = 40

speed of the Hamid ( x) = 50 km/h
speed of the Joseph ( y) = 40 km/h

Hence , the speed of the Hamid & Joseph is 50 km/ h & 40 km/h.

HOPE THIS WILL HELP YOU...

Answer 2

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