Problema Solution
The rate of a river’s current is 3 miles per hour. A boat traveled 24 miles down the river and then returned the same distance. The total time for the round trip was 6 hours. Find the rate of the boat in calm water.
Answer provided by our tutors
let
c = 3 mph the rate of a river’s current
v = the speed(rate) of the boat in calm water, v>0
d = 24 mi the distance the boat travels downstream = distance upstream
t1 = the time of the downstream trip
t2 = the time of the upstream trip
The total time for the round trip was 6 hours
t1 + t2 = 6
the speed of the boat when moving upstream is: v - c
the speed of the boat when moving downstream is: v + c
since speed = distance/time => time = distance/speed
t1= d/(v + c)
t1 = 24/(v + 3)
t2 = d/(v - c)
t2 = 24/(v - 3)
plug t1 = 24/(v + 3) and t2 = 24/(v - 3) into t1 + t2 = 6
24/(v + 3) + 24/(v - 3) = 6
by solving we find
v = 9 mph
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the rate of the boat in calm water is 9 mph.