Question

Points A and B are 90 km apart from each other on a highway. A car starts from A and another from B at the same time. If they go in the same direction they meet in 9 hours and if they go in opposite directions they meet in 9/4 hours. Find their speeds.

Answer 1

Let speed of car A be 'x' km/h

Let speed of car B be 'y' km/h

Now,

Ist Condition...( Given)

LET C BE THE MEETING POINT OF BOTH CARS

Let the distance covered by car A be AC

and Let the distance covered by B be BC

then, AC - BC = AB

(speed of car A × time taken by A) - (speed of car B × time taken by B) = 90

= ( X × 9) - ( Y× 9) = 90

= 9x-9y = 90

= x-y= 90/9

hence, x-y = 10..........(1)

Now,

II nd condition.....(Given)

Let C BE THE MEETING POINT OF BOTH CARS

then, AC+BC = AB

(speed of car A× time taken by A) - (speed of car B × time taken by B)

= (x × 9/4) + (y× 9/4) = 90

= 9/4x + 9/4y = 90

= 9/4 ( x+y ) = 90

= x + y = 90 × 4/9

= x+ y = 40........(2)

Now,

By elimination method........

x - y = 10.....(1)

x + y = 40..... (2)

2x = 50

x = 25

from......(2)

x + y = 40

then,

y = 40- 25

y= 15

hence,

The speed of Car A is 25km/h

The speed of Car B is 15 km/h