Alice travels 6 mph less than 2 times as fast as Mike starting at the same point and traveling in the same direction they are 187 miles apart after 5.5 hours find their speeds

Answer 1

Let's say Mike's speed is x mph.
According to the given information, Alice's speed is 2x - 6 mph.
The distance Mike travels in 5.5 hours is 5.5x miles.
The distance Alice travels in 5.5 hours is 5.5(2x - 6) miles.
Since they are 187 miles apart, we can set up the equation:
5.5x + 5.5(2x - 6) = 187
Expanding the equation:
5.5x + 11x - 33 = 187
Combining like terms:
16.5x - 33 = 187
Adding 33 to both sides:
16.5x = 220
Dividing both sides by 16.5:
x = 13.33
Mike's speed is approximately 13.33 mph.
Alice's speed is 2 * 13.33 - 6 = 20.67 mph.