iLikeFriedChicken: The boat could sail at 6 times the speed of the current in the river. Thus, the boat could go 100 miles upstream in 3 hours more than it took to go 14 miles downstream. What was the speed of the boat in still water?
What a great question.
Let the speed of the boat in still water be x miles/hour
then
the speed of the current must be x/6 miles/hour
When travelling against the current the speed will be (x-x/6) = 5x/6 miles/hour OR you can say 6/(5x) hours/mile
When travelling with the current the speed will be (x+x/6) = 7x/6 miles/hour OR you can say 6/(7x) hours/mile
The boat travels upstream 100miles
6/(5x) hours/mile * 100miles = 600/(5x) hours = 120/x hours. (The miles cancel out - and yes you can cancel the units like that)
The boat travels downstream 14 miles
6/(7x) hours/mile * 14 miles = 12/x hours
The boat travels 3 hours longer for the upstream journey so
12/x + 3 = 120/x
3 = 108/x
1/3 = x/108
108/3 = x
x = 36
So in still water the boat will travel at 36 miles/hour
+118725 
