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 after 9 hours and if they go in opposite directions, they meet after $\frac{9}{7}$ hours. The speeds (in km/hr) of A and B are

AB = 90 km

Let the speed of car starting from A be x kmph

and that of car starting from B be y kmph.

When cars move in the same direction and

meet at C.

Distance = Speed × Time

∴ 9x – 9y = AC – BC = AB

⇒ 9x – 9y = 90

⇒ x – y = 10... (i)

When they move in opposite directions,

$\frac{9 x}{7}+\frac{9 y}{7}=90$

$\Rightarrow x+y=10 \times 7=70 \ldots$ (ii)

On adding,

$2 x=80 \Rightarrow x=40 \mathrm{kmph}$

From equation (i)

$40-y=10 \Rightarrow y=40-10=30 \mathrm{kmph}$