Problema Solution
A boat traveled downstream a distance of 39 miles and then came right back. If the speed of the current was 12 miles per hour and the total trip took 4 hours and 20 minutes, find the average speed relative to the water.
Answer provided by our tutors
let
d = 39 mi the distance traveled in each directions
c = 12 mph the speed of the current
t = 4 hr 20 min = 4 + 20/60 hr = 4 + 1/3 hr
v = the speed of the boat relative to the water, v>0
since speed = distance/time follows time = distance/speed
d/(v + c) + d/(v - c) = t
39/(v + 12) + 39/(v - 12) = 4 + 1/3
by solving we find
v = 24 mph
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the average speed of the boat relative to the water is 24 miles per hour.