Problema Solution
A boat can travel 96 miles downstream in 2 hours and can make the return trip in 3 hours. Find the speed of the boat in still water.
Answer provided by our tutors
let
v = the speed of the boat in still water, v>0
c = speed of the current, c>0
d = 96 miles the distance the boat traveled one way
downstream speed: v + c
t1 = 2 h the time traveling downstream
upstream speed: v - c
t2 = 3h the time traveling upstream
since speed = distance/time
v + c = d/t1
v + c = 96/2
v - c = d/t2
v - c = 96/3
by solving the system of equations
v + c = 96/2
v - c = 96/3
we find
v = 40 mph
click here to see the step by step solution of the system of equations
the speed of the boat in still water is 40 miles per hour.