Problema Solution
A boat takes 5 hours to go 20 miles upstream. It can go 50 miles downstream in the same time. Find the rate of the current and the rate of the boat in still water. (Hint: Because the current pushes the boat when it is going downstream, the rate of the boat downstream is the sum of the rate of the boat and the rate of the current. The current slows down the boat when it is going upstream, so the rate of the boat upstream is the difference of the rate of the boat and the rate of the current.)
Answer provided by our tutors
Let
t = 5 hr the time of the travel in each direction
d1 = 20 mi the distance traveled upstream
d2 = 50 mi the distance traveled downstream
v = rate of the boat in still water, v>=0
r = the rate of the river, r>=0
We know that speed = distance/time
Traveling upstream the rate of the boat is: v - r
v - r = d1/t
v - r = 20/5
v - r = 4
Traveling downstream the rate of the boat is: v + r
v + r = d2/t
v + r = 50/5
v + r = 10
We have the following system of equations:
v - r = 4
v + r = 10
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v = 7 mph
r = 3 mph
The rate of the boat in still water is 7 mph.
The rate of the current is 3 mph.