The stillwater speed of the Faerie Queen was 4 times the spe

The still-water speed of the Faerie Queen was 4 times the speed of the current in the Lazy River. The Faerie Queen can travel 100 miles downstream in 1 hour more than she requires to travel 30 miles upstream. What is the still-water speed of the Faerie Queen and how fast does the Lazy River flow?

Solution

Let x=speed of current
Then 4x=still-water speed of the Faerie Queen
Speed downstream=4x+x=5x
Speed upstream=4x-x=3x
Distance (d)=rate(r) times time(t) or d=rt and t=d/r
Time downstream=100/5x
Time upstream=30/3x
Now we are told that the time to go 100 miles downstream (100/5x) minus 1 hour is equal to the time to go 30 miles upstream (30/3x). Thus, our equation to solve is:
(100/5x)-1=30/3x reduce the fractions:
(20/x)-1=10/x multiply both sides by x
20-x=10 subtract 20 from both sides:
-x=-10
x=10 mph-------------speed of the current
4x=4*10=40 mph ------------still water speed of theFaerie Queen