SOLUTION: Reed and his brother Ryan can put 9 mi between them in 20 min when starting fRom the same point and skating at top speed in opposite directions. It takes the same time for reed to

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Question 559586: Reed and his brother Ryan can put 9 mi between them in 20 min when starting fRom the same point and skating at top speed in opposite directions. It takes the same time for reed to pull a mile ahead of Ryan when they're skating in the same direction(again starting from the same point ).what is each one's top speed.thank you eight graders
Answer by AnlytcPhil(1806) (Show Source):
You can put this solution on YOUR website!

Let Reed's top speed be x miles per minute. Let Ryan's top speed be y miles per minute

Reed and his brother Ryan can put 9 mi between them in 20 min when starting fRom the same point and skating at top speed in opposite directions.

9mi per 20 minutes is or 0.45 miles per minute When separating in opposite directions, their rate of separation is x + y Therefore x + y = .45

It takes the same time for reed to pull a mile ahead of Ryan when they're skating in the same direction(again starting from the same point ).

1 mi per 20 minutes is or 0.05 miles per minute When separating in the same direction, their rate of separation is faster's rate minus slower's rate Therefore x - y = .05 x + y = .45 So the system of equations is x + y = .45 x - y = .05 ------------ 2x = .50 x = .25 x + y = .45 -x + y = -.05 ------------- 2y = .40 y = .20 Reed's rate = .25 miles/minute = = mile per minute. That's 1 mile in 4 minutes Ryan's rate = .20 miles/minute = = mile per minute. That's 1 mile in 5 minutes Edwin