SOLUTION: a boat can travel 42 miles upstream and 42 miles downstream in 10 hours. if the speed of the boat in still water is 10mph, what is the speed of the current. I'm not sure how to

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Question 268803: a boat can travel 42 miles upstream and 42 miles downstream in 10 hours. if the speed of the boat in still water is 10mph, what is the speed of the current.
I'm not sure how to re-arrange the formula for these variables, here's what I tried:
42+42/10=8.4 (presumably the average speed)
10mph-8.4mph=1.6(presumably the speed of the current)
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
a boat can travel 42 miles upstream and 42 miles downstream in 10 hours. if the speed of the boat in still water is 10mph, what is the speed of the current.
:
Although there is a certain logic in what you are doing, it's not right
Here is what they want I think
:
Let x = rate of the current
then
(10+x) = speed downstream
(10-x) = speed upstream
:
Write time equation; time = dist/speed
:
downstr time + upstr time = 10 hrs
+ = 10
:
multiply by (10+x)(10-x) to eliminate the denominators
42(10-x) + 42(10+x) = 10(10+x)(10-x)
:
420 - 42x + 420 + 42x = 10(100 - x^2)
:
840 = 1000 - 10x^2
:
10x^2 = 1000 - 840
10x^2 = 160
Simplify, divide by 10
x^2 = 16
x =
x = 4 mph is the current
:
:
Check solution by finding the time (14 mph down, 6 mph up)
42/14 = 3
42/6 = 7
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total = 10 hrs