Problema Solution
The speed of the current in a stream is 1 mi/hr. It takes a canoeist 36 minutes longer to paddle 2.4 miles upstream than to paddle the same distance downstream. What is the canoeist's rate in still water? (in mi/hr)
Answer provided by our tutors
distance = rate * time
let 'r' represent the canoeist's rate in still water, then 'r+1' represents the rate downstream and 'r-1' represents the rate upstream
36 minutes = 36/60 hours = 3/5
let 't' represent the time in hours it takes to paddle downstream, then 't+3/5' represents the time in hours to paddle upstream
we have these equations:
2.4 = (r+1)t, so t = 2.4/(r+1)
2.4 = (r-1)(t+3/5)
substituting 't' with '2.4/(r+1)' in the second equation gives:
2.4 = (r-1)((2.4/(r+1)) + 3/5)
solving for 'r' gives a positive value of r=3
the canoeist's rate in still water is 3mph