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Could you please show me the steps to the solution of this problem:
Gabrielle rows a boat downstream for 192 miles. The return trip upstream took 8 hours longer.
If the current flows at 2 mph, how fast does Gabrielle row in still water?
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The setup equation in the post by @josgarithmetic is incorrect.
The best what you can do with his post is to IGNORE it.
I came to bring the correct solution and describe the setup and steps clearly and in detailed way.
Ler "r" be the rate Gabrielle rows in still water (in miles per hour).
Then the effective rate downstream is (r+2) miles per hour and the time rowing downstream is hours.
The effective rate upstream is (r-2) miles per hour and the time rowing downstream is hours.
The difference of times is 8 hours, according to the condition. It gives you this time equation
- = 8 hours.
or, dividing both sides by 8, for simplicity
- = 1.
To solve this equation, multiply both sides by (r-2)*(r+2) = r^2 - 4. You will get
24*(r+2) - 24*(r-2) = r^2 - 4.
Simplify step by step
24r + 48 - 24r + 48 = r^2 - 4
r^2 = 48 + 48 + 4 = 100
r = = 10.
The problem is just solved.
The ANSWER is: the speed Gabrielle rows in still water is 10 miles per hour.
Let's CHECK. (in such problems, checking is very educative part of the solution.
When you check, your understanding of the problems becomes MUCH BETTER (!) )
The time rowing downstream is = = 16 hours.
The time rowing upstream is = = 24 hours.
The difference of times is 24 hours - 16 hours = 8 hours, exactly as stated in the problem.
Thus we checked and found out that the answer is CORRECT (!)
Solved and carefully explained.
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@josgaritmetic made changes in his post after seeing my solution.