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?
Algebra.Com
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
RELATED QUESTIONS
The current in a stream moves at a speed of 5 km/h. A boat travels 39 km upstream and 39... (answered by Alan3354)
A boat moves 28 km/h in still water. It travels 80 km upstream and 80 km downstream in a... (answered by mananth)
The speed of a boat in still water is 10 km/h. The boat travels 12 km upstream and 28 km... (answered by jorel1380)
A boat travels 60 km downstream in the same time that it takes to go 36 km upstream. The (answered by Paul)
The current in a stream moves at a speed of 3km/h. A boat travels 40 km upstream and 40... (answered by josmiceli)
The speed of a boat in still water is 15 km/h. The boat travels 40 km upstream and 40 km... (answered by scott8148)
The speed of a boat in still water is 9 km/h. The boat travels 72 km upstream and 72 km... (answered by ikleyn)
the speed of a boat in still water is 16 km/h.The boat travels 43 km upstream and 45 km... (answered by mananth)
a boat goes 16 km upstream and 24 km downstream in 6 hours. it also covers 12 km... (answered by ankor@dixie-net.com)