Alice travels 7 mph less than 2 times as fast as Mike starting at the same point and traveling in the same direction they are 171 miles apart after 4.5 hours find their speeds

Answer 1

Let's say Mike's speed is M mph.
Therefore, Alice's speed is (2M - 7) mph.
In 4.5 hours, Mike travels a distance of 4.5M miles.
In 4.5 hours, Alice travels a distance of 4.5(2M - 7) miles.
The total distance between them is the sum of the distances they traveled, which is 171 miles:
4.5M + 4.5(2M - 7) = 171
4.5M + 9M - 31.5 = 171
13.5M = 171 + 31.5
13.5M = 202.5
M = 202.5 / 13.5
M = <<15=15>>15 mph
Therefore, Mike's speed is 15 mph, and Alice's speed is 2(15) - 7 = 23 mph. Answer: \boxed{15 \text{ and } 23}.