SOLUTION: On a river a boat travels 240 miles downstream in the same amount of time that it takes to travel 160 miles upstream. The speed of the boat without current is 25 mph. Find the sp
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Question 106198: On a river a boat travels 240 miles downstream in the same amount of time that it takes to travel 160 miles upstream. The speed of the boat without current is 25 mph. Find the speed of the river. Be sure to define your variable, write an equation, and show how you solved it. Found 2 solutions by ptaylor, ankor@dixie-net.com:Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
distance(d) equals rate(r) times time(t) or d=rt; r=d/t and t=d/r
Let r=speed (rate) of the river
rate of the boat downstream=25+r
rate of the boat upstream=25-r
Time to travel downstream=(distance downstream)/(rate downstream)=240/(25+r)
Time to travel upstream=(distance upstream)/(rate upstream)=160/(25-r)
Now we are told that these two times are equal. So:
240/(25+r)=160/(25-r) multiply both sides by (25+r)(25-r)
240(25-r)=160(25+r) get rid of parens
6000-240r=4000+160r subtract 6000 and also 160r from both sides
6000-6000-240r-160r=4000-6000+160r-160r collect like terms
-400r=-2000 divide both sides by -400
r=5 mph-------------------rate (speed) of the river
CK
240/30=160/20
8=8
Hope this helps---ptaylor
You can put this solution on YOUR website! On a river a boat travels 240 miles downstream in the same amount of time that it takes to travel 160 miles upstream. The speed of the boat without current is 25 mph. Find the speed of the river.
:
Let x = speed of the river
Then
(25-x) = speed upstream
and
(25+x) = speed downstream
:
It tells us the times are equal, make a simple time equation from this fact:
Time = distance/speed
:
Time up = time down =
:
Cross multiply and you have:
160(25+x) = 240(25-x)
:
4000 + 160x = 6000 - 240x
:
160x + 240x = 6000 - 4000
:
400x = 2000
:
x = 2000/400
:
x = 5 mph is the current:
:
:
Check solution by seeing if, indeed, the times are the same:
Upstream: 160/20 = 8 hrs
Downstream: 240/30 = 8 hrs, confirms our solution
:
Make sense to you? Any questions?
