SOLUTION: The speed of a boat in still water is 8 km/h. It travels 60 km upstream and 60 km downstream in a total time of 16 hours. What is the speed of the stream?

Click here to see ALL problems on Rational-functions

Question 742105: The speed of a boat in still water is 8 km/h. It travels 60 km upstream and 60 km downstream in a total time of 16 hours. What is the speed of the stream?
Found 3 solutions by mananth, ankor@dixie-net.com, Alan3354:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website!
speed of stream =x
speed of boat in still water =8
time down stream = 60/(8+x)
time down stream = 60/(8-x)
time up + time down = 16 hours

Multiply equation by (8-x)(8+x)

x^2=4
x= +/- 2
ignore negative
x=2

Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website!
The speed of a boat in still water is 8 km/h.
It travels 60 km upstream and 60 km downstream in a total time of 16 hours.
What is the speed of the stream?
:
Let c = rate of the current
then
(8+c) = effective speed downstream
and
(8-c) = effective speed upstream
:
Write a time equation; time = dist/speed
:
Time upstr + time down = 16 hrs
+ = 16
multiply equation by (8-c)(8+c) canceling the denominators, you have
60(8-c) + 60(8+c) = 16(8-c)(8+c)
:
480 - 60c + 480 + 60c = 16(64-c^2)
:
960 = 1024 - 16c^2
:
16c^2 = 1024 - 960
16c^2 = 64
c^2 = 64/16
c^2 = 4
c =
c = 2 mph is the rate of the current
:
:
See if that checks out, find the actual time each way
60/6 = 10 hrs
60/10= 6 hrs
---------------
total 16 hrs

Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
The speed of a boat in still water is 8 km/h. It travels 60 km upstream and 60 km downstream in a total time of 16 hours. What is the speed of the stream?
-------------
Avg speed of a round trip = 2*r1*r2/(r1+r2) = 120/16 = 7.5
2*(8-c)*(8+c)/16 = 7.5

c = 2 km/hr