Question 1076121
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Let "u" and "v" be the Reed's and the Ryan's rates in miles per hour.


Then 

u + v = 27   (1)   (27 mph =  three times 9 miles per hour.
                        "Reed and Ryan can put 9 miles between them in 20 minutes when starting 
                         from the same point and sprinting at top speed in opposite directions")

u - v = 3    (2)   (3 mph = three times 1 mile per hour,
                        "It takes the same time for Reed to draw a mile ahead of Ryan when they're running in the same direction")


Add (1) and (2) to get u = {{{(27+3)/2}}} = 15 mph.

Then v = 27 - 15 = 12 mph.


<U>Answer</U>.  Reed' speed is 15 mph. Ryan' speed is 12 mph.
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