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.