Question

Points A and B are 90 km apart from each other on a highway. One car starts from A
and another from B at the same time. If the cars travel in the same direction at
different speeds they meet in 9 hours and if they travel towards each other they meet
in 9/7 hours. Find the speeds of the two cars.​

Answer 1

SOLUTION

Let the speed of cars A & B be x km/h & y km/hr respectively.

Let, speed of car A> speed of car B.

Case1:

Distance covered by car A in 9 hours=90km+ distance covered by car B in 9 hours

=) x km/hr ×9hr= 90km +y km/hr× 9hr

=) 9x= 90+9y

=) 9x-9y= 90

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

Case 2:

Distance covered by car A in 9/7 hr + Distance covered by car B in 9/7 hr= 90km

$= > x \: km / hr \times \frac{9}{7} hr + y \: km / hr \times \frac{9}{7}hr = 90 \\ = > \frac{9x}{7} + \frac{9y}{7} = 90 \\ = > 9x + 9y =630 \\ = > x + y = 70...........(2)$

Solving (1) & (2), we get

=) x-y= 10

x+y= 70---------(adding)

____________

=) 2x= 80

=) x= 80/2

=) x= 40km/hr

When x=40, we get

=) 40+y= 70......[using (2)]

=) y= 70-40

=) y= 30km/hr

Therefore,

Speed of car A= 40km/hr

Speed of car B= 30km/hr

Hope it helps ☺️