Problema Solution
A motorboat takes
5
hours to travel
100
mi
going upstream. The return trip takes
2
hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Answer provided by our tutors
Let
t1 = 5 hr the time of the travel upstream
t2 = 2 hr the time of the travel downstream
d =100 mi the distance traveled in each direction
v = rate of the boat in still water, v>0
r = the rate of the river
we know that speed = distance/time
traveling upstream the rate of the boat is v - r
v - r = d/t1
v - r = 100/5
traveling downstream the rate of the boat is: v + r
v + r = d/t2
v + r = 100/2
by solving the system of equations:
v - r = 100/5
v + r = 100/2
........
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........
v = 35 mph
r = 15 mph
The rate of the boat in still water is 35 mph.
The rate of the current is 15 mph.