Question 1204447
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The solutions in the three responses you have found are very similar, essentially using x and (2/3)x for the speeds of the two cyclists.<br>
Here is a different approach.<br>
The rates of the two cyclists are in the ratio 2:3, so the distances traveled by the two cyclists are in the ratio 2:3.  Using a standard method for setting up the problem for solving using that ratio....<br>
Let 2x = distance traveled by the slower cyclist
Let 3x = distance traveled by the faster cyclist<br>
The total distance was 25 miles:
2x+3x=25
5x=25
x=5<br>
The distances traveled by the two cyclists were 2x=10 and 3x=15 miles.<br>
Since the two cyclists met after 2 hours, their speeds were 10/2 = 5mph and 15/2 = 7.5mph<br>
ANSWER: 5mph and 7.5mph<br>