Man rowing boat

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Joe0430

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A man rowed upstream for 4 hours and returned to his starting point in 2 hours. If he rows 9 miles per hour in still water, find the rate of the stream.


Wouldn't the rate of the stream depend on the distance traveled? So is this not possible?
 
Distance = time times velocity
The two distances are the same so
4(9-r)=2(9+r)
 
That's right. When he's going up stream his still water speed is decreased by r to 9-r.
When he's going down stream his still water speed is increased by r to 9+r.
 
Hey

Gene,

How did you come up with "Distance = time times velocity
The two distances are the same so
4(9-r)=2(9+r)"?

I want to know the secret in terms of setting up equations from not so easy word problems?

Let's say a student decides to set up the equation this way:

4(9+r) = 2(9-r), what is the difference?
 
Joe0430 said:
A man rowed upstream for 4 hours and returned to his starting point in 2 hours. If he rows 9 miles per hour in still water, find the rate of the stream.
Click to expand...
Distance = Rate * Time

r = Rate of the stream

Upstream: DistanceUp = RateUp * TimeUp
Downstream: DistanceDown = RateDown * TimeDown

Rateup = 9 mph - r
RateDown = 9 mph + r

So, now we have:
Upstream: DistanceUp = (9 mph - r) * TimeUp
Downstream: DistanceDown = (9 mph + r) * TimeDown

TimeUp = 4 hrs
TimeDown = 2 hrs

So, now we have:
Upstream: DistanceUp = (9 mph - r) * (4 hrs)
Downstream: DistanceDown = (9 mph + r) * (2 hrs)

The last one is a little tricky.
"returned to his starting point" ==> DistanceUp = DistanceDown

So, now we have:
(9 mph - r) * (4 hrs) = (9 mph + r) * (2 hrs)

The student who wishes to get the correct answer will not set it up incorrectly. The "UP" time and rate go together and the "DOWN" time and rate go together. It doesn't work any other way.
 
Yes but...

Good job. I need for you to understand that not every student can think in this fashion. Can you understand that? Some people are very intelligent, even though you may not think so.
 
I need for you to understand that not every student can think in this fashion.
Click to expand...

Well, thinking that isn't going to get you anywhere.
 
Re: Yes but...

mathxyz said:
Good job. I need for you to understand that not every student can think in this fashion. Can you understand that? Some people are very intelligent, even though you may not think so.
Click to expand...
Cool down, buddy.
Your statements, related to the simplicity of the posted problem, make no sense...

If a student writes something down like 4+x = 2+x and sees nothing wrong, then the fault
lies with the teacher, or the student is obviously "slow";
got nothing to do with "fashion et al".
 
Re: Yes but...

mathxyz said:
I need for you to understand that not every student can think in this fashion. Can you understand that? Some people are very intelligent, even though you may not think so.
Click to expand...
We're not going to do this again, are we? Changing identity doesn't help?

I want to know the secret in terms of setting up equations from not so easy word problems? Let's say a student decides to set up the equation this way: 4(9+r) = 2(9-r), what is the difference?
Click to expand...
I answered the question that was presented. I would love to know why you think this is demeaning the student.
 
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