Jacqueline is 115 miles away from Miranda. They are traveling towards each other. If Miranda travels 9 mph faster than Jacqueline and they meet after 5 hours, how fast was each traveling?

If Jackie's speed is x, their combined speed is x + x+9 = 2x+9

The cover the 115 miles in 5 hours, so since distance = speed*time,

(2x+9)(5) = 115

Distance = 115 miles

Time taken = 5 hrs
Let jacqueline average speed be = a and miranda average speed = a + 9
Jacqueline a.s + miranda a.s = 2a + 9
from,
Average speed * time = distance
5(2a + 9) = 115
10a + 45 = 115
10a = 115 - 45
10a = 70
Divide both sides by 10
A = 7
Therefore jacqueline's speed was 7m/hr and miranda's speed was 7+9 = 16m/hr

To find the speeds at which Jacqueline and Miranda were traveling, we can use the formula Speed = Distance ÷ Time. Let's call Jacqueline's speed "x" mph. Since Miranda is traveling 9 mph faster than Jacqueline, we can represent Miranda's speed as "x + 9" mph.

Since they are traveling towards each other, the sum of their distances traveled will be equal to the total distance between them. Jacqueline traveled for 5 hours at a speed of x mph, so her distance traveled is 5x miles. Miranda also traveled for 5 hours, but at a speed of (x + 9) mph, so her distance traveled is 5(x + 9) miles.

The total distance between Jacqueline and Miranda is 115 miles. Therefore, we can set up the equation:

5x + 5(x + 9) = 115

Simplifying the equation, we get:

5x + 5x + 45 = 115
10x + 45 = 115

Now, we can solve for x:

10x = 115 - 45
10x = 70
x = 70 ÷ 10
x = 7

So, Jacqueline's speed was 7 mph, and since Miranda was traveling 9 mph faster, her speed was 7 + 9 = 16 mph.