# Current~ (Word Problem)

• May 10th 2011, 05:53 AM
Beastkun
Current~ (Word Problem)
A stream has a current of 4mph. Find the speed of Joe's boat in still water if it goes 40mph downstream in the same time it takes to go 24 miles upstream.

I think I solved this correctly but I would like a second opinion/verification.

-------------------------D----- R ------ T
UP---------------------24---- 4-x
DOWN -----------------40 --- 4+x

so 24/4-x = 40/4+x
96+24x=160-40x
24x=64-40x
64x=64
x=1?

Something about this problem seems off, but I'm not sure... any tips or verification would be nice.
• May 10th 2011, 06:30 AM
TheEmptySet
Quote:

Originally Posted by Beastkun
A stream has a current of 4mph. Find the speed of Joe's boat in still water if it goes 40mph downstream in the same time it takes to go 24 miles upstream.

I think I solved this correctly but I would like a second opinion/verification.

-------------------------D----- R ------ T
UP---------------------24---- 4-x
DOWN -----------------40 --- 4+x

so 24/4-x = 40/4+x
96+24x=160-40x
24x=64-40x
64x=64
x=1?

Something about this problem seems off, but I'm not sure... any tips or verification would be nice.

You have one small error. The speed of the boat up stream is

$x-4 \text{ not } 4-x$

This gives the equaiton

$\frac{24}{x-4}=\frac{40}{x+4}$

This will change the solution a bit.
• May 10th 2011, 02:16 PM
bjhopper
How can a boat go downstream with a helping current of 4mph unless its still water rate is 36mph
• May 10th 2011, 02:37 PM
topsquark
Quote:

Originally Posted by bjhopper
How can a boat go downstream with a helping current of 4mph unless its still water rate is 36mph

If you are getting 36 mph = 40 mph - 4 mph the 40 mph in the problem is a typo. It should be 40 miles. The boat is going x + 4 mph downstream and x - 4 mph upstream.

-Dan
• May 10th 2011, 03:05 PM
bjhopper
Dear Dan,

My statement is a wake up call to the OP and first responder. The upstream rate is 32 mph and the time to travel 24 mi is 3/4 hr. It makes no difference how far the boat goes downstream

bjh
• May 10th 2011, 03:14 PM
TheEmptySet
Quote:

Originally Posted by bjhopper
Dear Dan,

My statement is a wake up call to the OP and first responder. The upstream rate is 32 mph and the time to travel 24 mi is 3/4 hr. It makes no difference how far the boat goes downstream

bjh

Dear bhhopper:
I interpreted it as a typo because the problem is trivial if you already know the speed. This is standard problem in most algebra texts. Notice the table in the OP, this is used in many text books. We could ask Beastkun to clarify. The correct information is in the table!
• May 10th 2011, 04:34 PM
Wilmer
Quote:

Originally Posted by Beastkun
A stream has a current of 4mph. Find the speed of Joe's boat in still water if it goes 40mph downstream in the same time it takes to go 24 miles upstream.

Well, clearly a typo: 40 mph should be 40 miles.