<PRE><B>Question 196396</B>
    mary travels 45 miles up stream in 3 hours and travels 100 miles downstream in 4 hours. find the average speed of the boat in still water and the average speed of the current?
.
Applying the distance formula:
d = rt
where
d is distance
r is rate or speed
t is time
.
Let x = speed of boat in still water
and y = speed of current
.
Upstream:
3(x-y)= 45
dividing both sides by 3:
x - y = 15
.
Downstream:
4(x+y)= 100
dividing both sides by 4:
x + y = 25
.
Our system of equations:
x - y = 15 (equation 1)
x + y = 25 (equation 2)
.
Adding the two equations:
x - y = 15
x + y = 25
-----------
2x = 40
x = 20 mph (speed of boat in still waters)
.
substitute the above into equation 2 and solve for y:
x + y = 25
20 + y = 25
y = 5 mph (speed of current)</PRE>