The both left in opposite direction.
Therefotre we say, let Victoria's speed be represented by a mph
Then Racheal who travel in opposite direction with 9 hours faster is - ( a + 9 ) mph = ( - a - 9 ) mph
( please note that the above is negative because the directions are opposite and the 9 is included because it is 9 mph faster )
Next, we were told that the distance between them is 189 miles. We therefore need to subtract the distance covered by both of them and make it equal to 189 miles.
Since, distance = speed x time. And the time is 9 hours
The distance covered by Victoria therefore is ( a x 9 ) mph = 9a miles
The distance covered by Rachael therefore is 9 ( - a - 9 ) = - 9a - 81 miles
The distance between them therefore is ( -9a - 81 ) - 9a = 189
-9a - 9a - 81 = 189
-18a - 81 = 189
-18a = 189 + 81
-18a = 270
a = 270 / -18a ( divided both sides by 18a )
a = - 15
Therefore it is clear that victoria traveled with a speed of -15 mph
and Rachael who is - a - 9 = - ( -15 ) - 9 = 15 - 9 = 6 mph
Finally, we say Victoria travels at 15 mph and travels at 6 mph in the opposite direction.