Question

I am trying to help my son.
A canoe travels 4 miles per hour in still water. It travels 6 miles up stream and back again in 4 hours. what is the speed of the current?
He got an answer of 5.2
is that correct?

Answer 1

It cannot be correct because 5.2 is greater than 4, so he will never go upstream.
Let s= speed of current,
then
\[\frac{6}{4-s}+\frac{6}{4+s}=4\]
solve for s. (hint: reject negative root)

Answer 2

but it is less than 8 (4 up and 4 back again)

Answer 3

Im getting him......

Answer 4

Well, if you (are trying to) go upstream and can row at 4 mph. Current is rushing at you at 5.2 mph, you are going back at 1.2 mph, so you'll never get upstream. This has nothing to do with the 4 hours it takes to go up- and downstream.

Answer 5

if I scan his work, can you tell us where he went wrong?

Answer 6

it is not posting, it just hangs up

Answer 7

I scanned it as a different file type and it worked

Answer 8

He works well.
Everything is correct, except he made a minor mistake at the very beginning.
Knowing that he has to row upstream, we would expect that the current r should be less than 4.
The first line should read
6(4-r)+6(4+r)=4(4-r)(4+r)
and everything will turn out correctly.

Answer 9

THANK YOU!

Answer 10

You're welcome!

Answer 11

we ended up stuck again at
0=16-4r²

Answer 12

Divide by 4 on both sides:
\[0=4-r^2\]
add r^2 to both sides and take square-root
\[r^2=4\]
Let him try finishing the rest. (hint: reject negative root)

Answer 13

r=2

Answer 14

?

Answer 15

The answer is correct.
Check the time it takes to do the return trip:
6/(4-2)+6/(4+2)=3+1=4 hours...ok

Answer 16

are you available to tell me if he got the right answer on the next problem?

Answer 17

A boat travels 6 miles per hour in still water. It travels 8 miles upstream and back again in 8 hours. what is the speed of the current?
r=4.9

Answer 18

Correct to 1 decimal place.
To be exact, it is \[2\sqrt{6}=4.899...\]

Answer 19

yes! he rounded up. Again thank you. nothing like having a bunch of math I cant do that must be done by tomorrow in order to pass the class! 2 down, 15 to go