SOLUTION: A boat travels 30 miles upstream and 30 miles downstream. The total time for both parts of the trip is 8 hours. the speed of the boat in still water is 8 mph. Find the speed of the
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Question 473754: A boat travels 30 miles upstream and 30 miles downstream. The total time for both parts of the trip is 8 hours. the speed of the boat in still water is 8 mph. Find the speed of the current.
I have worked this problem 2 different ways and came up with 2 different answers both with radicals.
1. 30=(8+r)t <~~ I solved this one for t=30/(8+r)
30=(8-r)t
30=(8-r)(30/(8+r) the answer I got was 8+or- 2(squareroot of 15)
2. I used one from the website as a reference and worked it like this...
Current = X
upstream - x+8
downstream - 8-x
30/(x+8)+30/(8-x)= 8
LCM=(x+8)(8-x)
the answer I got was 2(squareroot of 31)
Where am I going wrong!? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A boat travels 30 miles upstream and 30 miles downstream.
The total time for both parts of the trip is 8 hours. the speed of the boat in still water is 8 mph.
Find the speed of the current.
:
x = the speed of the current like you said
then
(8+x) = speed downstream
and
(8-x) = speed upstream
:
Seems like you are on the right track here, let's just follow up this + = 8
multiply by (8+x)(8-x), resulting in
30(8-x) + 30(8+x) = 8(8-x)(8+x)
:
240 - 30x + 240 + 30x = 8(64 - x^2)
480 = 512 - 8x^2
8x^2 = 512 - 480
8x^2 = 32
divide by 8
x^2 = 4
x =
x = 2
:
:
Confirm this by finding the total times (upstr=6, downstr=10)
30/10 + 30/6 =
3 + 5 = 8
