julie travels 6 times faster then mill. Traveling in opposite directions, they are 714 miles apart afte 6 hours. Find the rate of travel

first represent unknowns using variables:

let x = rate of Mill
let x+6 = rate of Julie
recall that rate (or speed) is the distance travelled over time, or:
v = d/t
therefore, since 714 miles is their distance after 6 hours, and noting that they travel in opposite directions:
v = d/t
rearranging to get d:
d = vt
714 = 6x + 6(x+6)
*we add the distances they travelled because they travel in opposite directions,, solving:
714 = 6x + 6x + 36
678 = 12x
x = 56.5 miles per hour
x+6 = 62.5 miles per hour

hope this helps~ :)

To find the rate of travel, we can set up an equation using the formula:

Distance = Rate × Time.

Let's denote Mill's rate as 'x' (in miles per hour), and Julie's rate as '6x' (since Julie travels 6 times faster than Mill). We can also determine the time as 6 hours.

When traveling in opposite directions, their combined distances add up to the total distance, which in this case is 714 miles.

So, the equation becomes:

Mill's distance + Julie's distance = Total distance

(x × 6) + (6x × 6) = 714.

Now, let's solve for 'x':

6x + 36x = 714.

Combining like terms, we have:

42x = 714.

To solve for 'x', divide both sides of the equation by 42:

42x/42 = 714/42.

Simplifying:

x = 17.

Therefore, Mill's rate of travel is 17 miles per hour, and Julie's rate of travel is 6 times faster than that, which is 6 × 17 = 102 miles per hour.