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?

Answer 1

let the speed of the current be x mph
so rate upstream = 5-x mph
and rate downstream = 5+x mph

then
19/60 (5-x) = 13/60 (5+x)
19(5-x) = 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 round-off error)