A and b are two points 150 km apart

Asked by admin @ in Math viewed by 320 People

A and B are two points 150 km apart on a highwaytwo cars start with different speeds from A and B at the same time. if they move in the same Direction they meet in 15 hours but if they move in the opposite direction they meet in 1 hours. find their speed .

Answered by admin @


Hi !

Case I : When they travel in same direction

Speed of car starting from A = x km/hr
Time taken = 15 hrs
Distance travelled by A  = speed x time = 15x metres

Speed of car starting from B = y km/hr
Time taken = 15 hrs
Distance travelled by B  = speed x time = 15y metres

If they travel in same direction and reach  in same time , they reach at a point C
                    [ A picture is attached , refer to the pic 1 ]
We know that AB = 150 km
also , 
AC = 15x metres [ distance traveled by A ]
BC = 15y metres [ distance traveled by B]

AB = AC - BC
150 = 15x - 15y

15x - 15y = 150

x - y = 10             -----> (1)

----------------------------------------------------------

Case II : When they move in opposite directions :-

Speed of car A = x km/hr
Time taken = 1 hr
Distance = x metres

Speed of car B = y km/hr
Time taken = 1 hr
Distance = y metres

If they travel in opposite directions , they meet at a point C , between A and B [ refer to the pic 2 ]

x + y = 150             -----> (2)

---------------------------------------------

Solving equations 1 and 2 , we get 



x - y = 10
x + y = 150
----------

2x = 160

x = 80

x - y = 10

y = 70

-------------------------------------------------

Speed of car starting from A = 80 km/hr
Speed of car starting from B = 70 km/hr






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