Problema Solution
meg rowed her boat a distance of 19 mi and then rowed back to the starting point. the total time of the trip was 20 hours. if the rate of the current was 9 mph, find the average speed of the boat relative to the water
Answer provided by our tutors
let
d = 19 mi the distance in one direction
t = 20 hr the total time of the trip
c = 9 mph the rate of the current
v = the speed of the boat relative to the water, v>0
rowing with the current the speed of the boat is: v + c
rowing against the current the speed of the boat is: v - c
since speed = distance/time follows time = distance/speed:
the time of the trip downstream + the time of the trip upstream = the total time
d/(v - c) + d/(v + c) = t
19/(v - 9) + 19/(v + 9) = 20
by solving we find:
v = 10 mph
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the average speed of the boat relative to the water is 10 mph.