Let's say the speed of Carol is x mph.
The speed of Alice is 2x - 6 mph. (as Alice travels 6 mph less than 2 times as fast as Carol)
In 7.5 hours, Carol travels 7.5 * x = 7.5x miles.
In 7.5 hours, Alice travels 7.5 * (2x - 6) = 15x - 45 miles.
The total distance between them is the sum of the distances traveled by Carol and Alice:
7.5x + 15x - 45 = 292.5
22.5x - 45 = 292.5
22.5x = 337.5
x = 337.5 / 22.5
x = 15
Therefore, the speed of Carol is x = 15 mph.
The speed of Alice is 2x - 6 = 2 * 15 - 6 = 30 - 6 = 24 mph.
Alice travels 6 mph less than 2 times as fast as carol starting at the same point and traveling in the same direction they are 292.5 miles apart after 7.5 hours find their speeds
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