SOLUTION: Reed and his brother Ryan can put 9 miles between them in 20 minutes when starting from the same point and sprinting at top speed in opposite directions. It takes the same time for

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Question 1076121: Reed and his brother Ryan can put 9 miles between them in 20 minutes when starting from the same point and sprinting at top speed in opposite directions. It takes the same time for Reed to draw a mile ahead of Ryan when they're running in the same direction (again starting from the same point). what is each one's top speed?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
MILES and MINUTES

system%28r-b=1%2F20%2Cr%2Bb=9%2F20%29

Add those to find r.
Subtraction those to find b.

2r=%281%2B9%29%2F20
2r=10%2F20=1%2F2
r=1%2F4-----------------Reed runs 1 mile in 4 minutes.

Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
.
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 = %2827%2B3%29%2F2 = 15 mph.

Then v = 27 - 15 = 12 mph.


Answer.  Reed' speed is 15 mph. Ryan' speed is 12 mph.