Alice travels 6 times faster than Bill. Traveling in opposite directions, they are 714 miles apart after 6 hours. Find their rates of travel.
bill's speed --- x mph
Alice's speed -- 6x mph
After 5 hrs.
bill has gone 5x
Alice has gone 30x
5x+30x=714
x = 20.4
Bill went at 20.4 mph
Alice went at 122.4 mph
To find their rates of travel, let's start by setting up equations.
Let's assume Bill's rate of travel is x miles per hour. Since Alice travels 6 times faster than Bill, her rate of travel would be 6x miles per hour.
When traveling in opposite directions, their distances add up to the total distance between them:
Bill's distance = rate of travel * time = x * 6 = 6x miles
Alice's distance = rate of travel * time = 6x * 6 = 36x miles
According to the problem, the total distance between them after 6 hours is 714 miles:
Bill's distance + Alice's distance = 714 miles
6x + 36x = 714
Combining like terms, we get:
42x = 714
To isolate x, we divide both sides of the equation by 42:
x = 714 / 42
x = 17
So, Bill's rate of travel is 17 miles per hour.
Now, to find Alice's rate of travel, since she travels 6 times faster than Bill:
Alice's rate of travel = 6 * Bill's rate of travel = 6 * 17 = 102 miles per hour.
Therefore, Bill's rate of travel is 17 miles per hour, and Alice's rate of travel is 102 miles per hour.
Thus, Bill's rate of travel is 17 miles per hour, and Alice's rate of travel is 102 miles per hour.