Word problem equation help

Cindy Burgess

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Apr 13, 2013
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A trout can swim 48 feet downstream on a river in 3 seconds. It takes the trout 12 seconds to swim back upstream the same 48 feet. Find the speed of the current. Set up a system of equations. Downstream = x Upstream = y x-3=48 y+12=48 x-3=y+12 x=y+15 y=0, x=15 This is the best I can do. My textbook does not have an example of this for me to use.
 
Thank you

I'm printing your reply to study. Thank you. I'm just having "lots" of problems doing these word problems.
Let's be a bit more clear about this and use variables with meaningful names.

There are two things unknown here. The river current speed, vcurr, and the speed the fish can swim in still water, vfish.

Downstream we have 48 = (vfish+vcurr)*3

Upstream we have 48 = (vfish-vcurr)*12

Setting these two equal we get

(vfish+vcurr)*3 = (vfish-vcurr)*12

15 vcurr = 9 vfish,

5/3 vcurr = vfish

now 48 = (vfish+vcurr)*3 = vcurr(5/3+1)*3 = 8 vcurr,

vcurr=6 m/s

vfish = 5/3

vfish = 10 m/s

To check

(10+6)*3 = 48,
(10-6)*12 = 48

and we see we obtained the correct values
 
A trout can swim 48 feet downstream on a river in 3 seconds. It takes the trout 12 seconds to swim back upstream the same 48 feet. Find the speed of the current. Set up a system of equations. Downstream = x
This makes no sense because neither "Downstream" nor "x" has not been defined.

Upstream = y
This makes no sense because neither "Up stream" nor "y" has been defined. I think you meant to say "x is the trouts downstream speed, relative to the bank" and "y is the trout's upstream speed relative to the bank" but you need to be a lot more specific for other people to understand what you are saying.

If x is, in fact, the speed downstream, this is wrong. You cannot subtract "time" (3 seconds) from "speed". "Speed" is "distance divided by time (which is why we say "miles per hour" or "meters per second"). Rather, x= 48/3= 16 feet per second.

y+12=48
Similarly, y= 48/12= 4 feet per second.

x-3=y+12 x=y+15 y=0, x=15 This is the best I can do. My textbook does not have an example of this for me to use.

One thing that must be assumed here, that is not said, is that the trout swims at the same speed through the water. If we call the trout's speed through the water (or "relative to the water") "t" and the waters speed "v" then downstream the speed of the water is added to the trout's speed while upstream it is subtracted: x= t+v and y= t- v.

So your equations are t+ v= 16 and t- v= 4.
 
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