SOLUTION: At 9 pm, Lucy started to gallop her horse at 20 miles per hour to catch Edmund, who had a three hour head start, and if Lucy was still 30 miles behind at 11 om, how fast was Edmund

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Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=Edmund's rate of speed
Before Lucy started, Edmund had already travelled 3r miles.
In two hours, Lucy had travelled 20*2 or 40 miles
And in the same two hours, Edmund travelled another 2r miles
Now we are told that the distance Edmund travelled minus 30 mi equals the distance Lucy travelled, so:
5r-30=40 add 30 to each side
5r=70 divide each side by 5
r=14 mph----------------------------Edmund's rate of speed
CK
3*14+2*14-30=40
42+28-30=40
70-30=40
40=40

Hope this helps----ptaylor