Problema Solution
A rowing team rowed 60 miles while going with current in the same amount of time as it took to row 10 miles going against the current. The rate of the current was 5 miles per hour. Find the rate of the rowing team in still water.
Answer provided by our tutors
et
v = the rate of the rowing team in still water, v>0
c = 5 mph the rate of the current
d1 = 60 mi the distance traveled while doing with the current
d2 = 10 mi the distance traveled against the current
t = the time of the travel in one direction, t>0
the canoe's speed downstream: v + c = v + 5
the canoe's speed upstream: v - c = v - 5
since speed = distance/time => time = distance/speed
traveling downstream
t = d1/(v + c)
t = 60/(v + 5)
traveling upstream
t = d2/(v - c)
t = 10/(v - 5)
from t = 60/(v + 5) and t = 10/(v - 5) we have
60/(v + 5) = 10/(v - 5)
by solving we find
v = 7 mph
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the rate of the rowing team in still water is 7 miles per hour.