Posted by Kaley on .
A boy can row a boat at a constant rate of 5 mi/hr in still water. He rows upstream for 19 minutes and then rows downstream, returning to his starting point in another 13 minutes. What is the rate of the current? What is the total distance traveled?

Algebra 
Reiny,
let the speed of the current be x mph
so rate upstream = 5x mph
and rate downstream = 5+x mph
then
19/60 (5x) = 13/60 (5+x)
19(5x) = 13(5+x)
95  19x = 65 + 13x
30 = 32x
x = 30/32 mph or .9375 mph
total distance = 13/60(5.9375) = 1.296 miles each way.
check:
rate against current = 4.0625
rate with the current = 5.9375
time against current = 1.296/4.0625 = .316 hrs = 19.4 minutes
time with current = 1.296/5.9375 = .2183 = 13.1 minutes
(Acceptable roundoff error)